SAI_shortcut_1 {qlifetable}

Estimates seasonal-ageing indexes using shortcut 1.

Description

Given a set of data frames with the number of deaths recorded in a population/portfolio during several years (periods) in a set of integer ages for each combination of age and season/calendar quarter, this function approximates their corresponding seasonal-ageing indexes by employing shortcut 1, based on equation (2.5), proposed in Pavia and Lledo (2023).

Usage

SAI_shortcut_1(x, y, ..., margins = FALSE, min.age = 0, max.age = 100)

Arguments

x

A data frame with the number of deaths recorded in the population/portfolio during a period (typically a year) in a set of integer ages for each combination of age and season/calendar quarter. Usually, this is an output of the count_events_quarter function (or a data frame with the same structure).

y

A data frame with the number of deaths recorded in the population/portfolio during another period (typically a different year than the one corresponding to 'x') in a set of integer ages for each combination of age and season/calendar quarter. Usually, this is an output of the count_events_quarter function (or a data frame with the same structure).

...

Further data frames similar to 'x' and 'y' corresponding to another period(s)/year(s).

margins

A 'TRUE/FALSE' argument informing whether or not the marginal seasonal and ageing indexes should be also computed. Default, 'FALSE'.

min.age

A non-negative integer informing about the initial minimal age for which SAIs must be computed. This minimum age can be increased depending on the ages for which there are crude mx estimates (exposed-at-risk) in the objects 'x', 'y', '...'. Default, 0.

max.age

A positive integer informing about the initial maximum age for which SAIs must be computed. This maximum age can be decreased depending on the maximum ages for which there are crude mx estimates (exposed-at-risk) in the objects 'x', 'y', '...'. Default, 100.

Value

When 'margins = FALSE' a data frame with the (raw, normalized and linearized) estimated seasonal-ageing indexes (SAI) corresponding to the set of integer ages determined by 'min.age' and 'max.age' and the ages for which there is a least a death in the data frames introduced via the 'x', 'y' and '...' arguments for each combination of age and calendar quarter. The data frame has the following components:

age

Integer age to which the SAIs corresponds.

quarter.age

Age quarter to which the SAIs corresponds.

quarter.calendar

Calendar (time, season) quarter to which the SAIs corresponds.

SAI.raw

Estimates of raw seasonal-ageing indexes for each combination of 'age', 'quarter.age' and 'quarter.calendar'.

SAI.norm

Estimates of seasonal-ageing indexes, attained after normalizing raw SAIs estimates, for each combination of 'age', 'quarter.age' and 'quarter.calendar'.

SAI.lin

Final estimates of seasonal-ageing indexes, attained after linearizing normalized SAIs estimates, for each combination of 'age', 'quarter.age' and 'quarter.calendar'.

When 'margins = TRUE' the output is a list with three data frames 'SAI', 'SAI.age' and 'SAI.quarter'. 'SAI' is defined as just described above. 'SAI.age' and 'SAI.quarter' contains, in a similar vein than 'SAI', the estimated marginal SAIs, corresponding to, respectively, the age quarter and the calendar (time, season) quarter.

Author(s)

Jose M. Pavia [e-mail]

Josep Lledo [e-mail]

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. doi:10.1017/asb.2023.16

Examples

# This can take a while
 temp <- quarterly_variables(death_2006$date.birth, death_2006$date.death)
 e.death <- count_events_quarter(temp)
 SAI.example <- SAI_shortcut_1(e.death, e.death)

dates.b <- c("2017-05-13", "2018-04-12", "2018-01-01")
dates.d <- c("2020-09-23", "2021-10-11", "2021-11-23")
x <- quarterly_variables(dates.b, dates.d)
e.death <- count_events_quarter(x)
SAI.example <- SAI_shortcut_1(e.death, e.death)