Simulate severities from a truncated gamma distribution

Generate random claim severities from a gamma distribution conditional on the result falling inside the interval \((lower, upper)\).

Usage

rgammat(n, shape, scale, lower, upper)

Arguments

n

Integer. Number of observations to generate.

shape

Numeric. Shape parameter of the gamma distribution.

scale

Numeric. Scale parameter of the gamma distribution.

lower

Numeric. Lower truncation bound.

upper

Numeric. Upper truncation bound.

Value

A numeric vector of length n containing random draws from the truncated gamma distribution.

Details

Random values are generated by sampling from a uniform distribution on the interval \([F(lower), F(upper)]\), where \(F\) is the CDF of the gamma distribution, and then applying the inverse CDF.

The resulting sample follows the specified conditional distribution; values outside the truncation interval are not generated.

In severity analysis, this can be used for simulation and model checking when the available claims are observed only between a lower reporting threshold and an upper modelling limit. Truncation should not be confused with censoring or capping: the function assumes that values outside the interval are absent rather than recorded at a boundary.

See also

fit_truncated_severity(), rlnormt()

Author

Martin Haringa