Specify an empirical claim frequency distribution

Constructs the exact discrete distribution implied by observed claim counts or a weighted count table. No parametric distribution is fitted, no smoothing is applied, and unobserved counts receive probability zero.

Usage

empirical_frequency(data, count = NULL, weight = NULL, label = NULL)

Arguments

data

A nonempty numeric vector of observed nonnegative integer counts, or a data frame containing those counts.

count

For a data frame, an unquoted column containing the observed counts. Required for data-frame input and omitted for vector input.

weight

Optional nonnegative observation weights. For a data frame, provide an unquoted column; for a vector input, provide a numeric vector of the same length. When omitted, every row has weight one. Weights in a summarized frequency table may represent the number of policies having each claim count; they are not exposure offsets for fitting a rate.

label

Optional nonempty character scalar identifying the distribution.

Value

An object of classes "tidyact_frequency_spec" and "tidyact_distribution_spec", with the ordered fields schema_version, dist, params, support, data, custom, label, and metadata. The data field is a tibble::tibble() with columns count, weight, and probability, one row per count with positive empirical mass.

Details

If the observed counts are \(n_1,\ldots,n_m\) and their nonnegative weights are \(w_1,\ldots,w_m\), the empirical probability mass function is $$\widehat p_k = \frac{\sum_{i=1}^m w_i\,I(n_i=k)}{\sum_{i=1}^m w_i}.$$

At least one weight must be positive. Rows with zero weight do not contribute to the empirical support. Missing, negative, fractional, or nonfinite claim counts are rejected rather than silently discarded. Counts must not exceed \(2^{53}\), the largest consecutive integer representable exactly by an IEEE-754 double. Weights must be finite, nonnegative, and have a strictly positive finite total. Counts are kept in increasing order; no gaps in the observed set are filled with artificial positive probabilities.

This is the empirical distribution of the claim count per observational unit (such as a policy-year), not a table of individual claims. A vector of all ones describes a degenerate count distribution at one, not the total number of claims in a portfolio.

The result has the same lightweight S3 contract as frequency_spec(). Its dist field is "empirical"; params holds the finite count values and their exact empirical probabilities, and data contains the aggregated observed weights and probabilities. Only this compact frequency table is retained, not the original individual records.

The internal frequency registry provides the PMF, CDF, quantile function, RNG, raw and factorial moments, and probability generating function for this model. A general finite empirical frequency distribution is not assumed to belong to the Panjer \((a,b,0)\) class; its panjer operation is therefore unavailable. Other methods can use the same specification without silently fitting or approximating its probabilities.

See also

frequency_spec(), distribution_moments()

Examples

# One observation per policy-year: 0, 1, or 2 claims.
counts <- c(0, 0, 0, 1, 1, 2)
n <- empirical_frequency(counts)
n
#> <tidyact_frequency_spec>
#> Distribution: Empirical
#> Parameters:
#>   values: 0, 1, 2
#>   probs: 0.5000000, 0.3333333, 0.1666667
#> Support: {0, 1, ..., 2}
n$data
#> # A tibble: 3 × 3
#>   count weight probability
#>   <dbl>  <dbl>       <dbl>
#> 1     0      3       0.5  
#> 2     1      2       0.333
#> 3     2      1       0.167
distribution_moments(n, order = 1:3)
#> # A tibble: 3 × 4
#>   type  order value status
#>   <chr> <int> <dbl> <chr> 
#> 1 raw       1 0.667 finite
#> 2 raw       2 1     finite
#> 3 raw       3 1.67  finite
distribution_moments(n, order = 1:3, type = "factorial")
#> # A tibble: 3 × 4
#>   type      order value status
#>   <chr>     <int> <dbl> <chr> 
#> 1 factorial     1 0.667 finite
#> 2 factorial     2 0.333 finite
#> 3 factorial     3 0     finite

# The same empirical distribution as a summarized portfolio table.
portfolio <- tibble::tibble(
  claims = c(0, 1, 2),
  policies = c(3, 2, 1)
)
portfolio |>
  empirical_frequency(count = claims, weight = policies)
#> <tidyact_frequency_spec>
#> Distribution: Empirical
#> Parameters:
#>   values: 0, 1, 2
#>   probs: 0.5000000, 0.3333333, 0.1666667
#> Support: {0, 1, ..., 2}

# Unweighted data-frame input and a descriptive label.
observations <- tibble::tibble(claim_count = c(0, 1, 0, 2, 1))
observations |>
  empirical_frequency(count = claim_count, label = "Observed policy counts")
#> <tidyact_frequency_spec>
#> Distribution: Empirical
#> Parameters:
#>   values: 0, 1, 2
#>   probs: 0.4, 0.4, 0.2
#> Support: {0, 1, ..., 2}
#> Label: Observed policy counts