Package 'demor' reference manual

Title:	Methods for Demographic Analysis
Description:	Implements life tables, fertility and mortality indicators, decomposition methods, Lee-Carter mortality forecasting, Leslie matrices, and population pyramids for demographic analysis. Methods are described in Preston et al. (2001, ISBN:1557864519) and Ustyuzhanin (2025) <doi:10.17323/demreview.v12i4.30415>.
Authors:	Vadim Ustyuzhanin [aut, cre] (ORCID: <https://orcid.org/0000-0003-3800-1108>)
Maintainer:	Vadim Ustyuzhanin <[email protected]>
License:	MIT + file LICENSE
Version:	1.0.10
Built:	2026-05-27 22:38:41 UTC
Source:	https://github.com/vadvu/demor

Split continuous ages to age groups

Description

Split continuous ages to age groups

Usage

ages(x, groups, char = FALSE, below_min_val = NA)
ages(x, groups, char = FALSE, below_min_val = NA)

Arguments

x

Numeric array. Values of age that should be grouped

groups

Numeric array. Values of lower boundaries of age groups

char

Logical. Should output be numeric (FALSE) or character (TRUE)? By default, FALSE

below_min_val

What value to return for x < min(groups) when char = FALSE? Default is NA.

Value

If char = TRUE, a factor of the same length as x with age-group labels. Otherwise, a numeric vector of the same length as x with the lower boundaries from groups; values below the first group receive below_min_val.

Examples

groups <- c(0, 1, 5, 10, 15, 20, 24, 45, 85)
x <- 0:100
ages(x, groups, TRUE)

groups <- c(0, 1, 5, 10, 15, 20, 24, 45, 85)
x <- 0:100
ages(x, groups, TRUE)

Associated single decrement life table (ASDT) for causes of death (cause-deleted life table)

Description

Associated single decrement life table (ASDT) for causes of death (cause-deleted life table)

Usage

asdt(age, m_all, m_i, full = FALSE, method = "chiang1968", ...)
asdt(age, m_all, m_i, full = FALSE, method = "chiang1968", ...)

Arguments

age

Numeric array of age intervals; for full life table = 0:100; for concise life table = c(0:1, seq(5,85,5))

m_all

Numeric array with age specific mortality rates of all causes of death (usual mx).

m_i

Numeric array with age specific mortality rates of some cause of death (i)

full

Logical. Is full table needed? TRUE for full, FALSE for concise. By default, FALSE

method

Character. The method of ASDT construction to use. Now just "chiang1968" is supported.

...

Optional. Additional arguments for LT() function.

Value

If full = TRUE, a data frame with the full associated single decrement life table, including the standard life-table columns and the cause-deleted columns r_not_i, p_not_i, l_not_i, a_not_i, d_not_i, L_not_i, T_not_i, and ex_without_i. If full = FALSE, a reduced data frame with columns age, r_not_i, lx, qx, ax, ex, p_not_i, l_not_i, a_not_i, and ex_without_i.

References

Chiang, L. (1968). Introduction to Stochastic Processes in Biostatistics. New York: John Wiley and Sons.

Examples

data(asdtex)
asdt(
  age = asdtex$age,
  m_all = asdtex$all,
  m_i = asdtex$circulatory
)[1:3, ]
data(asdtex)
asdt(
  age = asdtex$age,
  m_all = asdtex$all,
  m_i = asdtex$circulatory
)[1:3, ]

Data on mortality of US men in 2002 by some causes

Description

Data on mortality of US men in 2002 by some causes

Usage

asdtex
asdtex

Format

A dataframe

age: age
neoplasms: age specific mortality rate (asmr) from Neoplasms
circulatory: asmr from Diseases of the circulatory system
respiratory: asmr from Diseases of the respiratory system
digestive: asmr from Diseases of the digestive system
other: asmr from other causes
all: overall asmr

Source

Andreev & Shkolnikov spreadsheet, can be seen on this webpage

Cohort Component Model for Projecting Population.

Description

Cohort Component Model for Projecting Population.

Usage

ccm(
  Mx.f,
  Mx.m = NULL,
  Fx,
  Ix.f = NULL,
  Ix.m = NULL,
  age.mx,
  age.fx,
  N0.f,
  N0.m = NULL,
  srb = 100/205,
  ...
)
ccm(
  Mx.f,
  Mx.m = NULL,
  Fx,
  Ix.f = NULL,
  Ix.m = NULL,
  age.mx,
  age.fx,
  N0.f,
  N0.m = NULL,
  srb = 100/205,
  ...
)

Arguments

Mx.f

Matrix or dataframe with mx for females, where row represents age, column represents a forecasted period. Thus, first column should be the first projected period, while each row represents age-specific mortality rate.

Mx.m

Optional. Matrix or dataframe with mx for males, where row represents age, column represents a forecasted period. Thus, first column should be the first projected period, while each row represents age-specific mortality rate.

Fx

Matrix or dataframe with fx, where row represents age, column represents a forecasted period. Thus, first column should be the first projected period, while each row represents age-specific fertility rate.

Ix.f

Optional. Matrix or dataframe with net number of female migrants, where row represents age, column represents a forecasted period. Thus, first column should be the first projected period, while each row represents net number of migrants.

Ix.m

Optional. Matrix or dataframe with net number of male migrants, where row represents age, column represents a forecasted period. Thus, first column should be the first projected period, while each row represents net number of migrants.

age.mx

Numeric vector. Age groups for Mx.f rows.

age.fx

Numeric vector. Age groups for Fx rows.

N0.f

Numeric vector. Female population in the initial period by age groups.

N0.m

Optional. Numeric vector. Male population in the initial period by age groups.

srb

Numeric. Sex ratio at birth for females. By default, it is 100/205.

...

Optional. Additional arguments for leslie() function.

Details

The model is calculated in matrix form as

$\mathbf{N}_{t+h} = \mathbf{L}_t(\mathbf{N}_{t} + \mathbf{I}_{t}/2) + \mathbf{I}_{t}/2$

where $\mathbf{N}_t$ is a column vector of population for time $t$ with $h$ as a step of projection (it is the length of age interval), $\mathbf{L}_t$ is Leslie matrix and $\mathbf{I}_{t}$ is a column vector of net migration.

Note that the model assumes that in $\mathbf{N}$ all age intervals are the same (i.e. $age = \{0-1, 1-4, 5-9, ...\}$ is not permitted). Fortunately (and thanks to me), the function handles such situations automatically by transforming all age groups into a unified standard.

Value

If Mx.m is NULL, a numeric matrix with projected female population, where rows are age groups and columns are periods 0:h. If male mortality is supplied, a list with matrices female, male, and all, each with the same row/column structure.

Examples

age.mx <- seq(0, 80, 5)
age.fx <- seq(15, 45, 5)
Mx.f <- matrix(
  rep(seq(0.005, 0.12, length.out = length(age.mx)), 2),
  nrow = length(age.mx),
  ncol = 2
)
Fx <- matrix(
  rep(c(0.02, 0.08, 0.11, 0.09, 0.05, 0.02, 0.005), 2),
  nrow = length(age.fx),
  ncol = 2
)
N0.f <- round(100000 * exp(-0.04 * age.mx))
ccm(Mx.f = Mx.f, Fx = Fx, age.mx = age.mx, age.fx = age.fx, N0.f = N0.f)
age.mx <- seq(0, 80, 5)
age.fx <- seq(15, 45, 5)
Mx.f <- matrix(
  rep(seq(0.005, 0.12, length.out = length(age.mx)), 2),
  nrow = length(age.mx),
  ncol = 2
)
Fx <- matrix(
  rep(c(0.02, 0.08, 0.11, 0.09, 0.05, 0.02, 0.005), 2),
  nrow = length(age.fx),
  ncol = 2
)
N0.f <- round(100000 * exp(-0.04 * age.mx))
ccm(Mx.f = Mx.f, Fx = Fx, age.mx = age.mx, age.fx = age.fx, N0.f = N0.f)

Age decomposition of mortality: single decrement process

Description

Age decomposition of mortality: single decrement process

Usage

decomp(mx1, mx2, sex = "m", age, method = "andreev", ax1 = NULL, ax2 = NULL)
decomp(mx1, mx2, sex = "m", age, method = "andreev", ax1 = NULL, ax2 = NULL)

Arguments

mx1

Numeric array with age specific mortality rates of population 1 (base population).

mx2

Numeric array with age specific mortality rates of population 2 (compared population).

sex

Character. Sex. "m" for males and "f" for females. By default, sex = "m".

age

Numeric array of age intervals; for full life table = 0:100; for concise life table = c(0:1, seq(5,85,5))

method

Character. Decomposition method. "andreev" (1982), "arriaga" (1984) or "pollard" (1982) - slightly different in their results. By default, method = "andreev".

ax1

Optional. Numeric array with ax for the 1st population. By default, it is a the middle of the interval, while ax for age 0 is modeled as in Andreev & Kingkade (2015).

ax2

Optional. Numeric array with ax for the 2nd population. By default, it is a the middle of the interval, while ax for age 0 is modeled as in Andreev & Kingkade (2015).

Details

Example of decomposition using Andreev (1982) formulas:

$\Delta_x = l_x^2(e_x^2 - e_x^1) - l_{x+n}^2(e_{x+n}^2 - e_{x+n}^1), \ \ \ x \neq \omega$

$\Delta_{\omega} = l_{\omega}^2(e_{\omega}^2 - e_{\omega}^1)$

where $\Delta_x$ is an absolute contribution of age $x$ to difference in $e_0$ between the second and the first population. $e_x^i, l_x^i$ are life table functions for population $i$ . $\omega$ is the last age group. Note, $e_0^2 - e_0^1 = \sum_{x}^{\omega}\Delta_x$

Value

A data frame with one row per age group. It always contains age, ex12, and ex12_prc, where ex12 is the absolute age contribution to the life-expectancy difference and ex12_prc is the percentage contribution. Additional columns depend on method and contain intermediate life-table quantities used in the decomposition.

References

Arriaga, E. E. (1984). Measuring and explaining the change in life expectancies. Demography, 21, 83-96.
Andreev, E. M. (1982). Metod komponent v analize prodolzhitel'nosti zhizni. Vestnik statistiki, 9, 42-47.
Pollard, J. H. (1982). The expectation of life and its relationship to mortality. Journal of the Institute of Actuaries, 109(2), 225–240.

Examples

age <- 0:5
mx1 <- c(0.02, 0.01, 0.012, 0.015, 0.02, 0.03)
mx2 <- c(0.018, 0.009, 0.011, 0.014, 0.019, 0.028)
decomp(mx1, mx2, age = age)$ex12
age <- 0:5
mx1 <- c(0.02, 0.01, 0.012, 0.015, 0.02, 0.03)
mx2 <- c(0.018, 0.009, 0.011, 0.014, 0.019, 0.028)
decomp(mx1, mx2, age = age)$ex12

e-dagger

Description

e-dagger

Usage

edagger(age, mx, ...)
edagger(age, mx, ...)

Arguments

age

Numeric array of age intervals

mx

Numeric array with age specific mortality rates.

...

Optional. Additional arguments for LT() function.

Value

A named numeric vector of the same length as age, where each element is ⁠e^\dagger_x⁠, the average remaining life years lost because of death from age x onward.

Examples

age <- 0:5
mx <- c(0.02, 0.01, 0.012, 0.015, 0.02, 0.03)
edagger(age, mx)[1:3]
age <- 0:5
mx <- c(0.02, 0.01, 0.012, 0.015, 0.02, 0.03)
edagger(age, mx)[1:3]

Fertility models for ASFR approximation

Description

Fertility models for ASFR approximation

Usage

fert.approx(fx, age, model, start = NULL, se = FALSE, alpha = 0.05, bn = 1000)
fert.approx(fx, age, model, start = NULL, se = FALSE, alpha = 0.05, bn = 1000)

Arguments

fx

Numeric vector of age specific fertility rates.

age

Numeric vector of ages.

model

Character. Model name to be estimated. Now "Hadwiger", "Gamma", "Brass" and "Beta" are supported.

start

Numeric vector with user-specific values of parameters for optimization. Default is NULL (choose automatically)

se

Logical. Should bootstrapped variance for ASFR approximation be calculated. Default is FALSE for no bootstrap.

alpha

Numeric. Used if se = TRUE, the level of uncertainty. By default, alpha = 0.05 for 95% CI.

bn

Numeric. Used if se = TRUE, number of bootstrap samples. By default, bn = 1000.

Details

This function runs least squares optimization (using default optim) of the selected fertility function with 1e-06 as tolerance parameter.

$f_x$ is age-specific fertility rate for age $x$ .

Hadwiger model

The model is as follows:

$f_x = \frac{ab}{c} \frac{c}{x}^{3/2} exp[-b^2(\frac{c}{x}+\frac{x}{c}-2)]$

where $a,b,c$ are estimated parameters that do not have demographic interpretation. Sometimes $c$ is interpreted as mean age at childbearing.

Gamma model

The model is as follows:

$f_x = \frac{R}{\Gamma(b)c^b}(x-d)^{b-1} exp[-(\frac{x-d}{c})]$

where $R,b,c,d$ are estimated parameters. $\Gamma$ is gamma function. $R$ can be interpreted as fertility level (TFR) and $d$ as mean age at childbearing.

Brass model

The model is as follows:

$f_x = c(x-d)(d+w-x)$

where $c,d,w$ are estimated parameters.

Beta model

The model is as follows:

$f_x = \frac{R}{B(A,C)}(\beta - \alpha)^{-(A+C-1)}(x-\alpha)^{(A-1)}(\beta-x)^{(B-1)}$

where $B(A, C)$ is beta function, $R, \beta, \alpha$ are estimated parameters, which can be interpreted as fertility level (TFR) and max and min age of childbearing respectively. $A,C$ are

$C = (\frac{(v - \alpha)(\beta - v)}{\tau^2} - 1)\frac{\beta - v}{\beta - \alpha}$

$A = C\frac{v-\alpha}{v - \beta}$

where $v, \tau^2$ are estimated parameters, where $v$ can be interpreted as mean age at childbearing. Thus, Beta model uses 5 parameters $R, \beta, \alpha, v, \tau^2$ , where only $\tau^2$ has no demographic interpretation.

Value

A list with two components: model, a list describing the fitted fertility model (type, fitted params, rmse, and, if se = TRUE, bootstrap covmat and parameter percentile intervals prc); and predicted, a data frame with observed and fitted age-specific fertility rates. When se = TRUE, predicted also includes bootstrap standard errors and percentile intervals.

References

Peristera, P., & Kostaki, A. (2007). Modeling fertility in modern populations. Demographic Research, 16, 141-194.

Examples

age <- seq(15, 45, 5)
fx <- c(0.03, 0.10, 0.14, 0.12, 0.07, 0.03, 0.01)
fert.approx(fx = fx, age = age, model = "Hadwiger", se = FALSE)
age <- seq(15, 45, 5)
fx <- c(0.03, 0.10, 0.14, 0.12, 0.07, 0.03, 0.01)
fert.approx(fx = fx, age = age, model = "Hadwiger", se = FALSE)

Download RosBris Data

Description

Download age-specific mortality, fertility, and population data from the Russian Fertility and Mortality Database (RosBris) and return them as long-format data frames for use in demor.

Usage

get_rosbris(
  dataset = c("mortality_1", "mortality_5", "fertility_1", "fertility_5"),
  refresh = FALSE
)
get_rosbris(
  dataset = c("mortality_1", "mortality_5", "fertility_1", "fertility_5"),
  refresh = FALSE
)

Arguments

dataset

Character. Dataset to download and parse. One of "mortality_1", "mortality_5", "fertility_1", or "fertility_5".

refresh

Logical. If FALSE (default), previously downloaded RosBris archives are reused from the local cache directory. If TRUE, archives are downloaded again from the RosBris website.

Details

The function downloads official .zip archives from the RosBris website, stores them in a user cache directory created by tools::R_user_dir(), reads .txt tables from the archives, and converts them to long-format data frames.

Returned data have the following structure:

"mortality_1": year, code, territory, sex, age, mx, N, Dx, name.
"mortality_5": year, code, territory, sex, age, mx, N, Dx, name.
"fertility_1": year, code, territory, age, fx, N, Bx, name.
"fertility_5": year, code, territory, age, fx, fx1, fx2, fx3, fx4, fx5, N, Bx, Bx1, Bx2, Bx3, Bx4, Bx5, name.

At the moment, get_rosbris() uses the legacy RosBris series corresponding to the periods 1989-2014 and 2015-2022. Updated post-census series are not used by this function.

Value

A data frame with one row per year-region-age combination. Column structure depends on dataset; see Details.

Source

Russian Fertility and Mortality Database. Center for Demographic Research, Moscow (Russia). Available at https://www.nes.ru/research-main/research-centers/demogr/demogr-fermort-data

Examples


if (interactive()) {
  mort <- get_rosbris("mortality_5")
  rus2010 <- subset(
    mort,
    year == 2010 & code == 1100 & sex == "m" & territory == "t"
  )
  head(rus2010)
}


if (interactive()) {
  mort <- get_rosbris("mortality_5")
  rus2010 <- subset(
    mort,
    year == 2010 & code == 1100 & sex == "m" & territory == "t"
  )
  head(rus2010)
}

Gini coefficient of a life table

Description

Gini coefficient of a life table

Usage

gini(age, mx, ...)
gini(age, mx, ...)

Arguments

age

Numeric array of age intervals

mx

Numeric array with age specific mortality rates.

...

Optional. Additional arguments for LT() function.

Value

A list with two components: Gini, itself a list with the relative Gini coefficient G0 and the absolute Gini coefficient G0_abs; and plot, a data frame with columns Fx and Phix for drawing the Lorenz curve.

Examples

age <- 0:5
mx <- c(0.02, 0.01, 0.012, 0.015, 0.02, 0.03)
gini(age, mx)$Gini
age <- 0:5
mx <- c(0.02, 0.01, 0.012, 0.015, 0.02, 0.03)
gini(age, mx)$Gini

The Human Life Indicator (HLI)

Description

The Human Life Indicator (HLI)

Usage

hli(age, mx, ...)
hli(age, mx, ...)

Arguments

age

Numeric array of age intervals; for full life table = 0:100; for concise life table = c(0:1, seq(5,85,5))

mx

Numeric array with age specific mortality rates.

...

Optional. Additional arguments for LT() function.

Details

It is calculated as

$HLI = \prod_{x=\alpha}^{\omega}(x + a_x)^{d_x}$

where $\alpha, \omega$ are the first and last age groups, $x$ is age, $a_x, d_x$ are life table functions (s.t. $\sum_{x=\alpha}^{\omega} d_x = 1$ ).

Value

A length-1 numeric value giving the Human Life Indicator, i.e. the geometric mean age at death implied by the life table.

References

Ghislandi, S., Sanderson, W.C., & Scherbov, S. (2019). A Simple Measure of Human Development: The Human Life Indicator. Population and Development Review, 45, 219–233.

Examples

age <- 0:5
mx <- c(0.02, 0.01, 0.012, 0.015, 0.02, 0.03)
hli(age, mx)
age <- 0:5
mx <- c(0.02, 0.01, 0.012, 0.015, 0.02, 0.03)
hli(age, mx)

Lee-Carter model

Description

Lee-Carter model

Usage

leecart(
  data,
  n = 10,
  alpha = 0.05,
  model = "RWwD",
  ax_method = "classic",
  bx_method = "classic",
  boot = FALSE,
  bn = 1000,
  ktadj = "none",
  ...
)
leecart(
  data,
  n = 10,
  alpha = 0.05,
  model = "RWwD",
  ax_method = "classic",
  bx_method = "classic",
  boot = FALSE,
  bn = 1000,
  ktadj = "none",
  ...
)

Arguments

data

Dataframe in the long format with the following columns: age, year, mx (age specific mortality rates). For some types of ktadj argument N (population at age x) and Dx (number of deaths at age x) columns should also be presented.

n

Numeric. Forecasted horizon

alpha

Numeric. The level of uncertainty. By default, alpha = 0.05 for 95% CI.

model

Character. Model type for kt forecasting. Can be "RWwD" for random walk with drift (by default, for original Lee-Carter model) or "ARIMA" for ARIMA model which parameters are chosen automatically by forecast::auto.arima().

ax_method

Character. Method for ax calculation. Can be "classic" from original Lee-Carter model (by default), "last" or "last_smooth". See details.

bx_method

Character. Method for bx calculation. Can be "classic" from original Lee-Carter model (by default) and "rotate" for rotating bx (Li et al., 2013).

boot

Logical. Should bootstrap estimates for uncertainty be used? FALSE by default.

bn

Numeric. Used if boot = TRUE, number of bootstrap samples. By default, bn = 1000.

ktadj

Character. Type of kt adjustment. It can be set to 'none' (defaukt, no adjustment), 'Dmin', 'e0min', 'poisson' or 'edaggermin' (see Details). Note that 'Dmin' and 'poisson' require data on the age-specific number of deaths (Dx column in the data) and the age-specific population (N column in the data).

...

Optional. Additional arguments for LT() function.

Details

The model argument specifies the forecasting method.

model ="RWwD" – classic random walk option
model = "ARIMA" for selecting a more complex time series model

The ax_method argument allows to control how a_x is calculated.

ax_method = "classic" – classic option with the average of the logarithm of mortality rates (but there is so-called "jump-off bias").
ax_method = "last" uses the logarithm of mortality for the last available year (as proposed in Lee & Miller, 2001).
ax_method = "last_smooth" uses data for the last year with smoothing (see Ševčíková et al., 2016, p. 288).

The bx_method argument allows to control how b_x is calculated.

bx_method = "classic" for the original method.
bx_method = "rotate" for the rotational variant (see Li et al., 2013).

The ktadj argument allows to control how k_t is calculated.

ktadj = "none" for no adjustment.
ktadj = "Dmin" for minimizing the deviance of predicted/actual annual deaths (as proposed in the original Lee-Carter paper). This method requires data on the age-specific number of deaths (Dx column in the data) and the age-specific population (N column in the data).
ktadj = "e0min" for minimizing the deviance of predicted/actual life expectancy (as proposed in Lee & Miller, 2001).
ktadj = "poisson" for minimizing the deviance from a Poisson model, where the dependent variable is the age-specific annual number of deaths (as proposed in Booth et al., 2002). This method requires data on the age-specific number of deaths (Dx column in the data) and the age-specific population (N column in the data).
ktadj = "edaggermin" for minimizing the deviance of predicted/actual edagger (see edagger()) as proposed in Rabbi & Mazzuco, 2021.

Value

A list with four components: model, the fitted time-series model used to forecast kt; kt, a data frame with historical and forecast mortality index values and confidence intervals; ex0, a data frame with observed, fitted, and forecast life expectancy at birth and confidence intervals; and mx, a data frame with observed, fitted, and forecast age-specific mortality rates and confidence intervals.

References

Booth, H., Maindonald, J., & Smith, L. (2002). Applying Lee-Carter under conditions of variable mortality decline. Population Studies, 56(3), 325-336. doi:10.1080/00324720215935

Lee, R. D., & Carter, L. R. (1992). Modeling and forecasting US mortality. Journal of the American Statistical Association, 87(419), 659–671. doi:10.1080/01621459.1992.10475265

Lee, R., & Miller, T. (2001). Evaluating the performance of the Lee-Carter method for forecasting mortality. Demography, 38(4), 537–549. doi:10.1353/dem.2001.0036

Li, N., Lee, R., & Gerland, P. (2013). Extending the Lee-Carter Method to Model the Rotation of Age Patterns of Mortality Decline for Long-Term Projections. Demography, 50(6), 2037–2051. doi:10.1007/s13524-013-0232-2

Rabbi, A. M. F., & Mazzuco, S. (2021). Mortality forecasting with the Lee-Carter method: Adjusting for smoothing and lifespan disparity. European Journal of Population, 37(1), 97-120. doi:10.1007/s10680-020-09559-9

Ševčíková, H., Li, N., Kantorová, V., Gerland, P., & Raftery, A. E. (2016). Age-Specific Mortality and Fertility Rates for Probabilistic Population Projections. In R. Schoen (Ed.), Dynamic Demographic Analysis (Vol. 39, pp. 285–310). Springer International Publishing. doi:10.1007/978-3-319-26603-9_15

Examples

age <- 0:20
year <- 2000:2009
lc_data <- expand.grid(age = age, year = year)
lc_data$mx <- exp(-7 + 0.09 * lc_data$age - 0.02 * (lc_data$year - min(year)))
fit <- leecart(lc_data, n = 2)
head(fit$kt)
age <- 0:20
year <- 2000:2009
lc_data <- expand.grid(age = age, year = year)
lc_data$mx <- exp(-7 + 0.09 * lc_data$age - 0.02 * (lc_data$year - min(year)))
fit <- leecart(lc_data, n = 2)
head(fit$kt)

Leslie Matrix

Description

Leslie Matrix

Usage

leslie(mx, fx, age.mx, age.fx, srb = 100/205, fin = TRUE, ...)
leslie(mx, fx, age.mx, age.fx, srb = 100/205, fin = TRUE, ...)

Arguments

mx

Numeric array of age specific mortality rates.

fx

Numeric array of age specific fertility rates.

age.mx

Numeric array of ages for mx.

age.fx

Numeric array of ages for fx.

srb

Numeric. Sex ratio at birth. Usually it is assumed that for males it is 105/205, for females it is 100/205. By default, it is 100/205.

fin

Logical. Should the survival rate for the last age-group be nonzero? By default it is FALSE, so the last survival rate is 0 as in classical model. Otherwise, it is $T_{x}/T_{x-1}$ .

...

Optional. Additional arguments for LT() function.

Value

A square numeric matrix of class leslie with one row and one column per age group. The first row contains fertility contributions and the subdiagonal contains survival ratios.

Examples

mx <- c(0.02, 0.01, 0.012, 0.015, 0.02)
fx <- c(0.05, 0.08)
leslie(mx = mx, fx = fx, age.mx = 0:4, age.fx = 1:2)
mx <- c(0.02, 0.01, 0.012, 0.015, 0.02)
fx <- c(0.05, 0.08)
leslie(mx = mx, fx = fx, age.mx = 0:4, age.fx = 1:2)

Life table

Description

Life table

Usage

LT(age, sex = "m", mx, ax = NULL, w = NULL, l0 = 1)
LT(age, sex = "m", mx, ax = NULL, w = NULL, l0 = 1)

Arguments

age

Numeric array of age intervals; for full life table = 0:100; for concise life table = c(0:1, seq(5,85,5))

sex

Character. Sex. "m" for males or "f" for females. By default = "m".

mx

Numeric array with age specific mortality rates.

ax

Optional. Numeric array with ax. By default, it is the middle of the interval, while ax for age 0 is modeled as in Andreev & Kingkade (2015).

w

Optional. Numeric array with weights for each age interval for calculating weighted life expectancy (wex).

l0

Numeric. Life table radix. By default, = 1 but it can be any positive real number. In "human" demography tradition it is 100'000, in "ecological" and "evolutionary" demography tradition it is 1.

Details

By default, $a_x$ for age 0 (first entity in ax) is modeled as in Andreev & Kingkade (2015, p. 390, see table 3-2).

The weighted life expectancy is calculated as follows:

$e_x^w = \frac{\sum_{i = x}^{\omega}L_x w_x}{l_x}$

where $\omega$ is the last age, $w$ is weight s.t. $w \in [0,1]$ , and other variables are life table functions.

Value

A numeric matrix with one row per age group. Standard columns are age, mx, ax, qx, lx, dx, Lx, Tx, and ex. If w is supplied, additional columns w, wLx, and wex are appended, where wex is weighted life expectancy.

References

Andreev, E. M., & Kingkade, W. W. (2015). Average age at death in infancy and infant mortality level: Reconsidering the Coale-Demeny formulas at current levels of low mortality. Demographic Research, 33, 363-390.

Examples

# Minimal toy example
age <- 0:5
mx <- c(0.02, 0.01, 0.012, 0.015, 0.02, 0.03)
LT(age = age, sex = "m", mx = mx)

if (interactive()) {
  # Real RosBris data via get_rosbris(): Russian males, 2010
  rus2010 <- subset(get_rosbris("mortality_5"),
    year == 2010 & code == 1100 & sex == "m" & territory == "t"
  )
  LT(age = rus2010$age, sex = "m", mx = rus2010$mx)
}

# Minimal toy example
age <- 0:5
mx <- c(0.02, 0.01, 0.012, 0.015, 0.02, 0.03)
LT(age = age, sex = "m", mx = mx)

if (interactive()) {
  # Real RosBris data via get_rosbris(): Russian males, 2010
  rus2010 <- subset(get_rosbris("mortality_5"),
    year == 2010 & code == 1100 & sex == "m" & territory == "t"
  )
  LT(age = rus2010$age, sex = "m", mx = rus2010$mx)
}

Mean Age at Childbearing (MAC)

Description

Mean Age at Childbearing (MAC)

Usage

mac(fx, age)
mac(fx, age)

Arguments

fx

Numeric array of age specific fertility rates.

age

Numeric array of ages. For example, 15:55 for 1-year age-groups

Value

A length-1 numeric value giving the mean age at childbearing implied by fx.

Examples

age <- seq(15, 45, 5)
fx <- c(0.03, 0.10, 0.14, 0.12, 0.07, 0.03, 0.01)
mac(fx, age)
age <- seq(15, 45, 5)
fx <- c(0.03, 0.10, 0.14, 0.12, 0.07, 0.03, 0.01)
mac(fx, age)

Age and cause decomposition of differences in life expectancies

Description

Age and cause decomposition of differences in life expectancies

Usage

mdecomp(mx1, mx2, age, method = "andreev", ...)
mdecomp(mx1, mx2, age, method = "andreev", ...)

Arguments

mx1

List of numeric arrays. 1st array should be all-cause nmx in the 1st population, other arrays are cause-specific nmx in the 1st population

mx2

List of numeric arrays. 1st array should be all-cause nmx in the 2nd population, other arrays are cause-specific nmx in the 2nd population

age

Numeric array of age intervals; for full life table = 0:100; for concise life table = c(0:1, seq(5,85,5))

method

Character. Decomposition method. "andreev" (1982) or "arriaga" (1984) - slightly different in their results. By default, method = "andreev".

...

Optional. Additional arguments for decomp().

Details

The contribution of each cause $c$ to the absolute difference in life expectancies between the first and second population is caculated as

$\Delta_{x,c} = \frac{m^1_{x,c} - m^2_{x,c}}{m^1_{x} - m^2_{x}} \times \Delta_{x}$

where $\Delta_{x}$ is contribution of age $x$ to difference $e_0^2 - e_0^1$ from function decomp(), $m^i_{x,c}$ is age-specific mortality rate for population $i$ from cause $c$ , and $m^i_x$ is total age-specific mortality rate.

Value

A data frame of class c("mdecomp", "data.frame") with one row per age group. Column age contains ages, ex12 contains the overall age contribution to the life-expectancy difference, and the remaining columns contain cause-specific contributions named after the cause-specific elements of mx1 and mx2.

Examples

data(mdecompex)
usa <- subset(mdecompex, cnt == "usa")
eng <- subset(mdecompex, cnt == "eng")
dec <- mdecomp(
  mx1 = list(
    all = usa$all,
    neoplasms = usa$neoplasms,
    circulatory = usa$circulatory
  ),
  mx2 = list(
    all = eng$all,
    neoplasms = eng$neoplasms,
    circulatory = eng$circulatory
  ),
  age = usa$age
)
dec[1:3, ]
data(mdecompex)
usa <- subset(mdecompex, cnt == "usa")
eng <- subset(mdecompex, cnt == "eng")
dec <- mdecomp(
  mx1 = list(
    all = usa$all,
    neoplasms = usa$neoplasms,
    circulatory = usa$circulatory
  ),
  mx2 = list(
    all = eng$all,
    neoplasms = eng$neoplasms,
    circulatory = eng$circulatory
  ),
  age = usa$age
)
dec[1:3, ]

Data on mortality of US and England and Wales men in 2002 by some causes

Description

Data on mortality of US and England and Wales men in 2002 by some causes

Usage

mdecompex
mdecompex

Format

A dataframe

age: age
neoplasms: age specific mortality rate (asmr) from Neoplasms
circulatory: asmr from Diseases of the circulatory system
respiratory: asmr from Diseases of the respiratory system
digestive: asmr from Diseases of the digestive system
other: asmr from other causes
all: overall asmr
cnt: country: usa - US, eng - England and Wales

Source

Andreev & Shkolnikov spreadsheet, can be seen on this webpage

Median age calculation

Description

Median age calculation

Usage

med.age(N, age)
med.age(N, age)

Arguments

N

Numeric array. Population counts by age groups (from young to old)

age

Numeric array. Lower bounds of age groups, same length as N

Value

A length-1 numeric value giving the estimated median age of the population represented by N.

Examples

N <- c(100, 90, 80, 70, 60)
age <- seq(0, 20, 5)
med.age(N, age)
N <- c(100, 90, 80, 70, 60)
age <- seq(0, 20, 5)
med.age(N, age)

Multiple Decrement Life Table

Description

Multiple Decrement Life Table

Usage

MLT(age, mx, ...)
MLT(age, mx, ...)

Arguments

age

Numeric array of age intervals; for full life table = 0:100; for concise life table = c(0:1, seq(5,85,5))

mx

List of numeric arrays. 1st array should be all-cause mx in the population, other arrays are cause-specific mx in the population.

...

Other parameters for the function LT() including ax (by default, the middle of the interval), sex (by default = "m" - males), l0 (by default = 1).

Value

A numeric matrix extending the output of LT(). In addition to the standard life-table columns, for each cause i in mx[-1] it adds qx_i, dx_i, lx_i, and ex_no_i, corresponding to cause-specific death probabilities, deaths, survivors, and cause-deleted life expectancy.

Examples

data(asdtex)
mx_causes <- list(
  all = asdtex$all,
  neoplasms = asdtex$neoplasms,
  circulatory = asdtex$circulatory
)
MLT(age = asdtex$age, mx = mx_causes)[1:3, c("age", "mx", "qx_neoplasms", "ex_no_neoplasms")]
data(asdtex)
mx_causes <- list(
  all = asdtex$all,
  neoplasms = asdtex$neoplasms,
  circulatory = asdtex$circulatory
)
MLT(age = asdtex$age, mx = mx_causes)[1:3, c("age", "mx", "qx_neoplasms", "ex_no_neoplasms")]

Mortality models for mx approximation

Description

Mortality models for mx approximation

Usage

mort.approx(mx, age, model = c("Brass", "Gompertz"), standard.mx = NULL, ...)
mort.approx(mx, age, model = c("Brass", "Gompertz"), standard.mx = NULL, ...)

Arguments

mx

Numeric vector of age specific mortality rates.

age

Numeric vector of ages.

model

Character. Model name to be estimated. Now "Gompertz" and "Brass" are supported.

standard.mx

Numeric vector of age specific mortality rates for standard population. Default is NULL.

...

Used only for Brass model. Other parameters for the function LT() including ax (by default, the middle of the interval), sex (by default = "m" - males), l0 (by default = 1).

Details

This function runs least squares optimization of the selected mortality function using Gauss-Newton algorithm algorithm with 2000 maximum iterations and 1e-07 as tolerance parameter. For "Gompertz" usual OLS estimator is used.

Gompertz model

The model is as follows:

$m(age) = \alpha e^{\beta age}$

Brass model

The model is as follows:

$y(age) = \alpha + \beta y^{S}(age)$

where

$y(age) = \frac{1}{2} ln[\frac{q(age)}{1-q(age)}]$

and subscript S defines that function is for standard population. To get mx from qx usual formula is used:

$m(age) = \frac{q(age)}{n-q(age)(n-a(age))}$

where n is the size of age interval and a(x) is a parameter from life table.

Value

A list with two components: model, the fitted lm or nls object; and predicted, a data frame with columns age and mx.pred containing the fitted mortality schedule.

References

Preston, S. H., Heuveline, P., & Guillot, M. (2001). Demography: Measuring and Modeling Population Processes. Blackwell Publishers.

Examples

age <- seq(40, 80, 10)
mx <- c(0.003, 0.005, 0.009, 0.018, 0.036)
standard.mx <- c(0.0025, 0.004, 0.007, 0.014, 0.03)
mort.approx(mx = mx, age = age, model = "Gompertz")
mort.approx(mx = mx, age = age, model = "Brass", standard.mx = standard.mx)
age <- seq(40, 80, 10)
mx <- c(0.003, 0.005, 0.009, 0.018, 0.036)
standard.mx <- c(0.0025, 0.004, 0.007, 0.014, 0.03)
mort.approx(mx = mx, age = age, model = "Gompertz")
mort.approx(mx = mx, age = age, model = "Brass", standard.mx = standard.mx)

Plot population pyramid

Description

Plot population pyramid

Usage

plot_pyr(
  popm,
  popf,
  popm2 = NULL,
  popf2 = NULL,
  age,
  prc = FALSE,
  sexn = c("Males", "Females"),
  sexc = c("#ED0000B2", "#00468BB2"),
  age.cont = NULL,
  un.intervals = TRUE
)
plot_pyr(
  popm,
  popf,
  popm2 = NULL,
  popf2 = NULL,
  age,
  prc = FALSE,
  sexn = c("Males", "Females"),
  sexc = c("#ED0000B2", "#00468BB2"),
  age.cont = NULL,
  un.intervals = TRUE
)

Arguments

popm

Numeric vector of male population

popf

Numeric vector of female population

popm2

Optional. Numeric vector of second male population to be plotted as line.

popf2

Optional. Numeric vector of second female population to be plotted as line.

age

Numeric vector of ages

prc

Should the population be shown as a percentage rather than in absolute terms? By default, it is FALSE and the plot shows user-specific values in popm and popf.

sexn

Character array of labels for the sexes. By default = c("Males", "Females")

sexc

Character array of colors for the sexes. By default = c("#ED0000B2","#00468BB2"), which are red and blue

age.cont

Optional. Logical. Should the age axis be considered as continuous scale? Recommend to switch to TRUE if the age intervals are small (1 year) and FALSE otherwise (for ex., when age interval is 5 years). By default function chooses the value by itself.

un.intervals

Logical. Should the age groups be unified? For example, if the first and second groups are 0-1, 1-4, and all other groups are five-year, the function automatically makes the group 1-4 to make all the intervals the same. By default, TRUE.

Value

A ggplot2 object representing a population pyramid. If popm2 and popf2 are supplied, the plot also includes dashed comparison lines for the second population.

Examples

plot_pyr(
  popm = c(100, 90, 80, 70, 60),
  popf = c(95, 92, 85, 75, 65),
  age = seq(0, 20, 5)
)
plot_pyr(
  popm = c(100, 90, 80, 70, 60),
  popf = c(95, 92, 85, 75, 65),
  age = seq(0, 20, 5)
)

Plot for mdecomp function

Description

Plot for mdecomp function

Usage

## S3 method for class 'mdecomp'
plot(x, return.data = FALSE, ...)
## S3 method for class 'mdecomp'
plot(x, return.data = FALSE, ...)

Arguments

x

A result of age and cause decomposition from mdecomp().

return.data

Should the data be returned (TRUE) or the ggplot2 plot (default, FALSE).

...

Ignored.

Value

If return.data = FALSE, a ggplot2 object with stacked bars of age- and cause-specific contributions. If return.data = TRUE, a data frame with columns age, ex12, and group used to build the plot.

Examples

data(mdecompex)
usa <- subset(mdecompex, cnt == "usa")
eng <- subset(mdecompex, cnt == "eng")
dec <- mdecomp(
  mx1 = list(
    all = usa$all,
    neoplasms = usa$neoplasms,
    circulatory = usa$circulatory
  ),
  mx2 = list(
    all = eng$all,
    neoplasms = eng$neoplasms,
    circulatory = eng$circulatory
  ),
  age = usa$age
)
plot(dec)
data(mdecompex)
usa <- subset(mdecompex, cnt == "usa")
eng <- subset(mdecompex, cnt == "eng")
dec <- mdecomp(
  mx1 = list(
    all = usa$all,
    neoplasms = usa$neoplasms,
    circulatory = usa$circulatory
  ),
  mx2 = list(
    all = eng$all,
    neoplasms = eng$neoplasms,
    circulatory = eng$circulatory
  ),
  age = usa$age
)
plot(dec)

Rosbris' Region codes

Description

Rosbris' Region codes

Usage

rosbris.codes
rosbris.codes

Format

A dataframe

n: number of Region (sequence number)
name: Region name
code: Region unique code

Source

Russian Fertility and Mortality Database. Center for Demographic Research, Moscow (Russia). Available at https://www.nes.ru/demogr-fermort-data

Data on Standard Life expectancies that is used for YLL calculations

Description

Data on Standard Life expectancies that is used for YLL calculations

Usage

sle_stand
sle_stand

Format

A dataframe

stand: Standard: 1 - World Health Organization Standard Life Expectancy by single-age; 2 - Global Burden of Disease studies (GBD) and WHO Global Health Estimates (WHO GHE) Standard Life Expectancy by 5-year age groups.
age: age
ex: Standard Life Expectancy

Source

Martinez, R., Soliz, P., Caixeta, R., Ordunez, P. (2019). Reflection on modern methods: years of life lost due to premature mortality-a versatile and comprehensive measure for monitoring non-communicable disease mortality. International Journal of Epidemiology, 48, 1367-1376. doi:10.1093/ije/dyy254

Leslie matrix summary

Description

Leslie matrix summary

Usage

## S3 method for class 'leslie'
summary(object, d = 1, ...)
## S3 method for class 'leslie'
summary(object, d = 1, ...)

Arguments

object

A leslie matrix from leslie().

d

Time step. By default it is 1. Only affects $r$ .

...

Ignored.

Details

The function calculates $\lambda$ , $r$ , $w$ and $v$ .

$\lambda$ – asymptotic growth factor that is dominant eigenvalue.
$r$ – asymptotic growth rate that is $ln \lambda / \delta t$ .
$w$ – stable age distribution normalized to 1 s.t. $\sum_x^{\omega} w_x = 1$ where $x$ is age.
$v$ – reproductive values normalized s.t. $v'w = 1$ .

Value

A list of class summary.leslie with four components: lambda (dominant eigenvalue / asymptotic growth factor), r (intrinsic growth rate), w (stable age distribution summing to 1), and v (reproductive values normalized so that sum(v * w) = 1).

Examples

mx <- c(0.02, 0.01, 0.012, 0.015, 0.02)
fx <- c(0.05, 0.08)
les <- leslie(mx = mx, fx = fx, age.mx = 0:4, age.fx = 1:2)
summary(les)

mx <- c(0.02, 0.01, 0.012, 0.015, 0.02)
fx <- c(0.05, 0.08)
les <- leslie(mx = mx, fx = fx, age.mx = 0:4, age.fx = 1:2)
summary(les)

Tempo-adjusted total fertility rate (TFR')

Description

Tempo-adjusted total fertility rate (TFR')

Usage

tatfr(past_fx, present_fx, post_fx, age)
tatfr(past_fx, present_fx, post_fx, age)

Arguments

past_fx

List with numeric arrays of age specific fertility rates for period t-1 by parity

present_fx

List with numeric arrays of age specific fertility rates for period t by parity (it is period of interest)

post_fx

List with numeric arrays of age specific fertility rates for period t+1 by parity

age

Array with numeric values age

Details

This indicator is calculated as follows

$TFR_{i,t}' = \frac{TFR_{i,t}}{1-(M_{i,t+1} - M_{i,t-1}) / 2}$

where $TFR_{i,t}', TFR_{i,t}$ are tempo-adjusted and usual total fertility rate for parity $i$ and time $t$ respectively, $M_{i,t}$ is mean age at childbearing for parity $i$ and time $t$ . The tempo-adjusted total fertility rate is a sum of parity-specific $TFR_i'$ .

Note, the calculation are done as in footnote 1 in (Bongaarts & Feeney, 2000, p. 563). Unfortunately, the original 1998 article does not provide the exact formula, which has caused some confusion in academic circles.

Value

A list with four components: tatfr (overall tempo-adjusted total fertility rate), tatfr_i (parity-specific tempo-adjusted rates), tfr (overall conventional TFR), and tfr_i (parity-specific conventional rates).

References

Bongaarts, J., & Feeney, G. (1998). On the Quantum and Tempo of Fertility. Population and Development Review, 24(2), 271–291. doi:10.2307/2807974

Bongaarts, J., & Feeney, G. (2000). On the Quantum and Tempo of Fertility: Reply. Population and Development Review, 26(3), 560–564. doi:10.1111/j.1728-4457.2000.00560.x

Examples

age <- seq(15, 45, 5)
past_fx <- list(
  c(0.02, 0.05, 0.07, 0.05, 0.03, 0.01, 0.00),
  c(0.01, 0.03, 0.04, 0.03, 0.02, 0.01, 0.00)
)
present_fx <- list(
  c(0.03, 0.06, 0.08, 0.06, 0.03, 0.01, 0.00),
  c(0.01, 0.03, 0.05, 0.04, 0.02, 0.01, 0.00)
)
post_fx <- list(
  c(0.03, 0.05, 0.08, 0.07, 0.04, 0.02, 0.00),
  c(0.01, 0.03, 0.04, 0.04, 0.03, 0.01, 0.00)
)
tatfr(past_fx, present_fx, post_fx, age)
age <- seq(15, 45, 5)
past_fx <- list(
  c(0.02, 0.05, 0.07, 0.05, 0.03, 0.01, 0.00),
  c(0.01, 0.03, 0.04, 0.03, 0.02, 0.01, 0.00)
)
present_fx <- list(
  c(0.03, 0.06, 0.08, 0.06, 0.03, 0.01, 0.00),
  c(0.01, 0.03, 0.05, 0.04, 0.02, 0.01, 0.00)
)
post_fx <- list(
  c(0.03, 0.05, 0.08, 0.07, 0.04, 0.02, 0.00),
  c(0.01, 0.03, 0.04, 0.04, 0.03, 0.01, 0.00)
)
tatfr(past_fx, present_fx, post_fx, age)

Total Fertility Rate (TFR)

Description

Total Fertility Rate (TFR)

Usage

tfr(fx, age.int = 1)
tfr(fx, age.int = 1)

Arguments

fx

Numeric array of age specific fertility rates.

age.int

Numeric. Age group: 1 for one-year, 5 for five-year. Any age groups are allowed.

Value

A length-1 numeric value equal to the sum of age-specific fertility rates multiplied by age.int.

Examples

fx <- c(0.02, 0.08, 0.12, 0.09, 0.04, 0.01, 0.001)
tfr(fx, age.int = 5)
fx <- c(0.02, 0.08, 0.12, 0.09, 0.04, 0.01, 0.001)
tfr(fx, age.int = 5)

Years of Life Lost (YLL) calculation

Description

Years of Life Lost (YLL) calculation

Usage

yll(
  Dx,
  type = c("yll", "yll.p", "yll.r", "asyr"),
  age.int = 5,
  Dx_all = NULL,
  pop = NULL,
  w = NULL,
  standard = NULL
)
yll(
  Dx,
  type = c("yll", "yll.p", "yll.r", "asyr"),
  age.int = 5,
  Dx_all = NULL,
  pop = NULL,
  w = NULL,
  standard = NULL
)

Arguments

Dx

Array with the number of deaths.

type

Character. Type of YLL to calculate. See details section.

age.int

Numeric. Age interval of Dx. Can be 1 or 5.

Dx_all

Array with the number of all deaths. Used only with yll.p type, where Dx is array with cause-specific deaths.

pop

Array with population. Used only with yll.r and asyr types.

w

Array with population weights for direct standardization. Used only with asyr type.

standard

Data frame. User-specific standard life expectancy to calculate YLL with the following columns: age, ex. Note: the age.int argument should be consistent with the age column in this data frame.

Details

Computes four types of Years of Life Lost (YLL) indicators:

Absolute YLL (type = "yll"):

$YLL_{x,t,c} = D_{x,t,c} \times SLE_x$

where $x,t,c$ are age, time, and cause respectively, $D_{x,t,c}$ is deaths in age $x$ at time $t$ from cause $c$ and $SLE_x$ is standard life expectancy at age $x$
YLL proportion (type = "yll.p"):

$YLL_{x,t,c}^p = \frac{YLL_{x,t,c}}{YLL_{x,t}}$

where $YLL_{x,t} = \sum_{c} YLL_{x,t,c}$ (total YLL across causes)
YLL rate (type = "yll.r"):

$YLL_{x,t,c}^r = \left( \frac{YLL_{x,t,c}}{N_{x,t}} \right) \times 100'000$

where $N_{x,t}$ is population in age group $x$ at time $t$
Age-standardized YLL rate (type = "asyr"):

$ASYR_{t,c} = \sum_{x=\alpha}^{\omega} \left( YLL_{x,t,c}^r \times w_x \right)$

where $\alpha$ to $\omega$ corresponds to first to last age group, $w_x$ is standard population weight for age $x$ .

Value

A list whose components depend on type. For type = "yll", the list contains yll_all (overall YLL) and yll (age-specific YLL). For type = "yll.p", it contains yll.p_all and yll.p (overall and age-specific YLL proportions). For type = "yll.r", it contains yll.r_all and yll.r (overall and age-specific YLL rates). For type = "asyr", it contains asyr_all and asyr (overall and age-specific age-standardized YLL rates).

References

Martinez, R., Soliz, P., Caixeta, R., & Ordunez, P. (2019). Reflection on modern methods: years of life lost due to premature mortality—a versatile and comprehensive measure for monitoring non-communicable disease mortality. International Journal of Epidemiology, 48, 1367–1376.

Examples

yll(Dx = rep(1, 19), type = "yll", age.int = 5)$yll_all
yll(Dx = rep(1, 19), type = "yll", age.int = 5)$yll_all

Package 'demor'

Help Index

Split continuous ages to age groups

Description

Usage

Arguments

Value

Examples

Associated single decrement life table (ASDT) for causes of death (cause-deleted life table)

Description

Usage

Arguments

Value

References

Examples

Data on mortality of US men in 2002 by some causes

Description

Usage

Format

A dataframe

Source

Cohort Component Model for Projecting Population.

Description

Usage

Arguments

Details

Value

Examples

Age decomposition of mortality: single decrement process

Description

Usage

Arguments

Details

Value

References

See Also

Examples

e-dagger

Description

Usage

Arguments

Value

Examples

Fertility models for ASFR approximation

Description

Usage

Arguments

Details

Hadwiger model

Gamma model

Brass model

Beta model

Value

References

Examples

Download RosBris Data

Description

Usage

Arguments

Details

Value

Source

See Also

Examples

Gini coefficient of a life table

Description

Usage

Arguments

Value

Examples

The Human Life Indicator (HLI)

Description

Usage

Arguments

Details

Value

References

Examples

Lee-Carter model

Description