Fit severity distributions to truncated claim data

Estimate an underlying claim severity distribution when the observed claims are truncated.

Usage

fit_truncated_severity(
  losses = NULL,
  distribution = c("gamma", "lognormal"),
  lower_truncation = NULL,
  upper_truncation = NULL,
  start_values = NULL,
  print_initial = TRUE,
  n_variants = 1,
  n_shape_grid = 8,
  n_scale_grid = 8,
  show_progress = FALSE,
  show_summary = TRUE,
  y = NULL,
  dist = NULL,
  left = NULL,
  right = NULL,
  start = NULL,
  trace = NULL,
  report = NULL
)

Arguments

losses

Numeric vector with observed claim severities.

distribution

Severity distribution to fit: "gamma" or "lognormal".

lower_truncation

Numeric lower truncation point. Claims at or below this value are assumed not to be present in losses. Defaults to 0.

upper_truncation

Numeric upper truncation point. Claims at or above this value are assumed not to be present in losses. Defaults to Inf.

start_values

Optional named list of starting values. If NULL, a multi-start strategy is used. For a gamma distribution use shape and scale; for a lognormal distribution use meanlog and sdlog.

print_initial

Deprecated logical retained for backward compatibility.

n_variants

Controls how many local variations around base starts are used.

n_shape_grid

Number of grid points for gamma shape.

n_scale_grid

Number of grid points for gamma scale.

show_progress

Logical. If TRUE, prints periodic progress during the fitting loop.

show_summary

Logical. If TRUE, prints a short summary at the end.

y, dist, left, right, start, trace, report

Deprecated argument names kept for backward compatibility.

Value

An object of class c("truncated_severity", "truncated_dist", "fitdist"). The object contains the fitted distribution parameters from fitdistrplus::fitdist() and additional attributes:

truncated_vec

The observed losses used for fitting.

lower_truncation, upper_truncation

The truncation bounds.

fit_attempts

Metadata for each attempted start combination.

n_attempts, n_success, n_failed

Fit attempt counts.

best_attempt_index

Index of the selected start combination.

Details

In insurance pricing, severity models are often fitted on claim amounts that are not observed over the full range of possible losses. Small claims may be absent because of a deductible, reporting threshold, or data extraction rule. Very large claims may be capped, excluded, or modelled separately as large losses. A standard gamma or lognormal fit on the remaining observed claims treats that truncated sample as if it were complete, which can bias the estimated severity distribution.

fit_truncated_severity() fits the distribution conditional on the claim being observed within the truncation interval. This means the fitted likelihood uses the density divided by the probability mass between lower_truncation and upper_truncation. The function is intended for truncation, where claims outside the interval are absent from the data. This differs from censoring, where claims outside a limit are still observed but their exact amount is not known.

Observed losses must lie strictly inside the truncation interval. Values outside the interval indicate that the bounds do not describe the data and therefore produce an error.

Examples

if (FALSE) { # \dontrun{
observed <- MTPL2$amount[MTPL2$amount > 500 & MTPL2$amount < 10000]
fit <- fit_truncated_severity(
  losses = observed,
  distribution = "gamma",
  lower_truncation = 500,
  upper_truncation = 10000
)
autoplot(fit)
} # }