Benktander type II distribution
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] |
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).
See also
- Weibull distribution
- Benktander type I distribution
Notes
- ^ a b From Wolfram Alpha
References
- 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.
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Probability distributions (list)
univariate
with finite support | |
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with infinite support |
univariate
univariate
continuous- discrete |
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(joint)
- Discrete:
- Ewens
- multinomial
- Continuous:
- Dirichlet
- multivariate Laplace
- multivariate normal
- multivariate stable
- multivariate t
- normal-gamma
- Matrix-valued:
- LKJ
- matrix normal
- matrix t
- matrix gamma
- Wishart
- Univariate (circular) directional
- Circular uniform
- univariate von Mises
- wrapped normal
- wrapped Cauchy
- wrapped exponential
- wrapped asymmetric Laplace
- wrapped Lévy
- Bivariate (spherical)
- Kent
- Bivariate (toroidal)
- bivariate von Mises
- Multivariate
- von Mises–Fisher
- Bingham
and singular
- Degenerate
- Dirac delta function
- Singular
- Cantor
- Category
- Commons