The Benktander type II distribution, also called the Benktander distribution of the second kind, is one of two distributions introduced by Gunnar Benktander (1970) to model heavy-tailed losses commonly found in non-life/casualty actuarial science, using various forms of mean excess functions (Benktander & Segerdahl 1960). This distribution is "close" to the Weibull distribution (Kleiber & Kotz 2003).
Probability density function | |||
Cumulative distribution function | |||
Parameters |
(real) (real) | ||
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Support | |||
CDF | |||
Mean | |||
Median |
Where is the Lambert W function[note 1] | ||
Mode | |||
Variance |
Where is the generalized Exponential integral[note 1] |