crude_mx_sh3: Data frame(s) of crude estimates of quarterly (and annual) central rates of mortality estimated using shortcut 3.

Description

Computes for a general/insured population crude estimates of quarterly (and annual) central rates of mortality by age (in a set of integer ages) for each combination of age and calendar quarter, using quarterly age aggregated data of population stocks and age-season quarterly counts of deaths, immigrants/new policies (entries) and emigrants/lapses/expirations (exits) by employing shortcut 3, based on equation (2.9), proposed in Pavia and Lledo (2023).

Usage

crude_mx_sh3(
  pop.start,
  pop.end,
  events.death,
  events.out,
  events.in,
  annual = FALSE
)

Value

When `annual = FALSE` a data frame with estimated crude central rates of mortality for each combination of age and calendar quarter in the set of integer ages determined by the intersection of ages in `pop.start` and `pop.end`. The data frame has the following components:

age: Integer age to which the crude central rate of mortality corresponds.
quarter.age: Age quarter to which the crude central rate of mortality corresponds.
quarter.calendar: Calendar (time, season) quarter to which the crude central rate of mortality corresponds.
exposed: Total exposure-at-risk times in the target population, calulated according to shortcut 2, for each combination of `age`, `quarter.age` and `quarter.calendar`.
deaths: Number of deaths in the target population for each combination of `age`, `quarter.age` and `quarter.calendar`.
mx: Estimated crude central rate of mortality corresponding to the combination of `age`, `quarter.age` and `quarter.calendar`.

When `annual = TRUE` the output is a list with two data frames `mx.quarterly` and `mx.annual`. `mx.quarterly` is a data frame with the estimated quarterly crude central rates of mortality as just described and `mx.annual` is the corresponding data frame with the estimated annual crude central rates of mortality.

Arguments

pop.start: A data frame, corresponding to the target population/portfolio, containing by age the stock of population/portfolio by quarter collected at the beginning of the year. This data frame must have three columns. The first refers to integer ages (e.g., 20, 21, 22,...), the second to the quarter (with values 1, 2, 3 and 4) and the third to the number of people in the population/portfolio at the beginning of the year corresponding to each integer age and quarter.
pop.end: A data frame, corresponding to the target population/portfolio, containing by age the stock of population/portfolio by quarter collected at the end of the year. This data frame must have three columns. The first refers to integer ages (e.g., 20, 21, 22,...), the second to the quarter (with values 1, 2, 3 and 4) and the third to the number of people in the population/portfolio at the end of the year corresponding to each integer age and quarter.
events.death: A data frame with the number of deaths recorded in the population/portfolio during the target year in a set of integer ages for each combination of age and season/calendar quarter. Typically, this is an output of the function count_events_quarter or a data frame with the same structure. If the range of ages in `events.death` does not cover the range of ages in the intersection of ages defined by `pop.start` and `pop.end`, zeros are imputed for the missing ages.
events.out: A data frame with the number of exits (emigrants/lapses/expirations) recorded in the population/portfolio during the target year in a set of integer ages for each combination of age and season/calendar quarter. Typically, this is an output of the function count_events_quarter or a data frame with the same structure. If the range of ages in `events.out` does not cover the range of ages in the intersection of ages defined by `pop.start` and `pop.end`, zeros are imputed for the missing ages.
events.in: A data frame with the number of entries (immigrants/new policies) recorded in the population/portfolio during the target year in a set of integer ages for each combination of age and season/calendar quarter. Typically, this is an output of the function count_events_quarter or a data frame with the same structure. If the range of ages in `events.in` does not cover the range of ages in the intersection of ages defined by `pop.start` and `pop.end`, zeros are imputed for the missing ages.
annual: A character string informing whether the annual crude central rates of mortality should also be computed. Default, `FALSE`.

Author

Jose M. Pavia pavia@uv.es

Josep Lledo josep.lledo@uv.es

References

Pavia, JM and Lledo, J (2023). Shortcuts for the construction of sub-annual life tables. *ASTIN Bulletin: The Journal of the International Actuarial Association*, 53(2), 332-350. tools:::Rd_expr_doi("10.1017/asb.2023.16")

Examples

Run this code

# \donttest{
# This can take a while
 pop <- 2005 - as.numeric(substr(pop_2006$date.birth, 1 , 4))
 pop <- as.data.frame(table(pop))
 pop[, 1] <- as.numeric(as.character(pop[, 1]))
 pop[, 2] <- pop[, 2]/4
 pop <- cbind(apply(pop, 2, rep, each = 4), quarter = rep(1:4, nrow(pop)))[, c(1, 3, 2)]
 pop <- as.data.frame(pop)
 temp <- quarterly_variables(death_2006$date.birth, death_2006$date.death)
 e.death <- count_events_quarter(temp)
 temp <- quarterly_variables(emi_2006$date.birth, emi_2006$date.emi)
 e.emi <- count_events_quarter(temp)
 temp <- quarterly_variables(immi_2006$date.birth, immi_2006$date.immi)
 e.immi <- count_events_quarter(temp)
 out <- crude_mx_sh3(pop, pop, e.death, e.emi, e.immi)
# }
pop.1 <- data.frame(age = c(rep(40, 4), rep(41, 4)), quarter = rep(1:4, 2), people = c(4134, 4353))
pop.2 <- data.frame(age = c(rep(40, 4), rep(41, 4)), quarter = rep(1:4, 2), people = c(4250, 4213))
dates.b <- c("1980-04-12")
dates.d <- c("2020-08-23")
x <- quarterly_variables(dates.b, dates.d)
e.death <- count_events_quarter(x)
dates.b <- c("1980-05-12")
dates.e <- c("2020-06-23")
x <- quarterly_variables(dates.b, dates.e)
e.emi <- count_events_quarter(x)
dates.b <- c("1980-07-12")
dates.i <- c("2020-12-10")
x <- quarterly_variables(dates.b, dates.i)
e.immi <- count_events_quarter(x)
out <- crude_mx_sh3(pop.1, pop.2, e.death, e.emi, e.immi)

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