trx_stats: Summarize transactions and utilization rates

In actxps: Create Actuarial Experience Studies: Prepare Data, Summarize Results, and Create Reports

Summarize transactions and utilization rates

Description

Create a summary data frame of transaction counts, amounts, and utilization rates.

Usage

trx_stats(
  .data,
  trx_types,
  percent_of = NULL,
  combine_trx = FALSE,
  col_exposure = "exposure",
  full_exposures_only = TRUE,
  conf_int = FALSE,
  conf_level = 0.95
)

## S3 method for class 'trx_df'
summary(object, ...)

Arguments

.data	A data frame with exposure-level records of type exposed_df with transaction data attached. If necessary, use as_exposed_df() to convert a data frame to an exposed_df object, and use add_transactions() to attach transactions to an exposed_df object.
trx_types	A character vector of transaction types to include in the output. If none is provided, all available transaction types in .data will be used.
percent_of	A optional character vector containing column names in .data to use as denominators in the calculation of utilization rates or actual-to-expected ratios.
combine_trx	If FALSE (default), the results will contain output rows for each transaction type. If TRUE, the results will contains aggregated experience across all transaction types.
col_exposure	Name of the column in .data containing exposures
full_exposures_only	If TRUE (default), partially exposed records will be excluded from data.
conf_int	If TRUE, the output will include confidence intervals around the observed utilization rate and any percent_of output columns.
conf_level	Confidence level for confidence intervals
object	A trx_df object
...	Groups to retain after summary() is called

Details

Unlike exp_stats(), this function requires data to be an exposed_df object.

If .data is grouped, the resulting data frame will contain one row per transaction type per group.

Any number of transaction types can be passed to the trx_types argument, however each transaction type must appear in the trx_types attribute of .data. In addition, trx_stats() expects to see columns named ⁠trx_n_{*}⁠ (for transaction counts) and ⁠trx_amt_{*}⁠ for (transaction amounts) for each transaction type. To ensure .data is in the appropriate format, use the functions as_exposed_df() to convert an existing data frame with transactions or add_transactions() to attach transactions to an existing exposed_df object.

Value

A tibble with class trx_df, tbl_df, tbl, and data.frame. The results include columns for any grouping variables and transaction types, plus the following:

• trx_n: the number of unique transactions.

• trx_amt: total transaction amount

• trx_flag: the number of observation periods with non-zero transaction amounts.

• exposure: total exposures

• avg_trx: mean transaction amount (trx_amt / trx_flag)

• avg_all: mean transaction amount over all records (trx_amt / exposure)

• trx_freq: transaction frequency when a transaction occurs (trx_n / trx_flag)

• trx_utilization: transaction utilization per observation period (trx_flag / exposure)

If percent_of is provided, the results will also include:

• The sum of any columns passed to percent_of with non-zero transactions. These columns include the suffix ⁠_w_trx⁠.

• The sum of any columns passed to percent_of

• ⁠pct_of_{*}_w_trx⁠: total transactions as a percentage of column ⁠{*}_w_trx⁠. In other words, total transactions divided by the sum of a column including only records utilizing transactions.

• ⁠pct_of_{*}_all⁠: total transactions as a percentage of column ⁠{*}⁠. In other words, total transactions divided by the sum of a column regardless of whether or not transactions were utilized.

If conf_int is set to TRUE, additional columns are added for lower and upper confidence interval limits around the observed utilization rate and any percent_of output columns. Confidence interval columns include the name of the original output column suffixed by either ⁠_lower⁠ or ⁠_upper⁠.

• If values are passed to percent_of, an additional column is created containing the the sum of squared transaction amounts (trx_amt_sq).

"Percentage of" calculations

The percent_of argument is optional. If provided, this argument must be a character vector with values corresponding to columns in .data containing values to use as denominators in the calculation of utilization rates or actual-to-expected ratios. Example usage:

• In a study of partial withdrawal transactions, if percent_of refers to account values, observed withdrawal rates can be determined.

• In a study of recurring claims, if percent_of refers to a column containing a maximum benefit amount, utilization rates can be determined.

Confidence intervals

If conf_int is set to TRUE, the output will contain lower and upper confidence interval limits for the observed utilization rate and any percent_of output columns. The confidence level is dictated by conf_level.

• Intervals for the utilization rate (trx_util) assume a binomial distribution.

• Intervals for transactions as a percentage of another column with non-zero transactions (⁠pct_of_{*}_w_trx⁠) are constructed using a normal distribution

• Intervals for transactions as a percentage of another column regardless of transaction utilization (⁠pct_of_{*}_all⁠) are calculated assuming that the aggregate distribution is normal with a mean equal to observed transactions and a variance equal to:

  Var(S) = E(N) * Var(X) + E(X)^2 * Var(N),

  Where S is the aggregate transactions random variable, X is an individual transaction amount assumed to follow a normal distribution, and N is a binomial random variable for transaction utilization.

Default removal of partial exposures

As a default, partial exposures are removed from .data before summarizing results. This is done to avoid complexity associated with a lopsided skew in the timing of transactions. For example, if transactions can occur on a monthly basis or annually at the beginning of each policy year, partial exposures may not be appropriate. If a policy had an exposure of 0.5 years and was taking withdrawals annually at the beginning of the year, an argument could be made that the exposure should instead be 1 complete year. If the same policy was expected to take withdrawals 9 months into the year, it's not clear if the exposure should be 0.5 years or 0.5 / 0.75 years. To override this treatment, set full_exposures_only to FALSE.

summary() Method

Applying summary() to a trx_df object will re-summarize the data while retaining any grouping variables passed to the "dots" (...).

Examples

expo <- expose_py(census_dat, "2019-12-31", target_status = "Surrender") |>
  add_transactions(withdrawals)

res <- expo |> group_by(inc_guar) |> trx_stats(percent_of = "premium")
res

summary(res)

expo |> group_by(inc_guar) |>
  trx_stats(percent_of = "premium", combine_trx = TRUE, conf_int = TRUE)

actxps documentation built on June 26, 2024, 9:07 a.m.