Benktander type I distribution

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Benktander distribution of the first kind
Parameters (real)
Variance [note 1]

The Benktander type I distribution 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). The distribution of the first type is "close" to the lognormal distribution (Kleiber & Kotz 2003).



  • Kleiber, Christian; Kotz, Samuel (2003). "7.4 Benktander Distributions". Statistical Size Distributions in Economics and Actuarial Science. Wiley Series and Probability and Statistics. John Wiley & Sons. pp. 247–250. ISBN 9780471457169. 
  • Benktander, Gunnar; Segerdahl, Carl-Otto (1960). "On the Analytical Representation of Claim Distributions with Special Reference to Excess of Loss Reinsurance". Proceedings of the XVIth International Congress of Actuaries, Brussels, 1960: 626–646. 
  • Benktander, Gunnar (1970). "Schadenverteilungen nach Grösse in der Nicht-Lebensversicherung" [Loss Distributions by Size in Non-life Insurance]. Bulletin of the Swiss Association of Actuaries (in German): 263–283.