The Delaporte distribution is a

discrete probability distribution In probability theory and statistics, a probability distribution is a function that gives the probabilities of occurrence of possible events for an experiment. It is a mathematical description of a random phenomenon in terms of its sample spa ...

that has received attention in

actuarial science Actuarial science is the discipline that applies mathematics, mathematical and statistics, statistical methods to Risk assessment, assess risk in insurance, pension, finance, investment and other industries and professions. Actuary, Actuaries a ...

. It can be defined using the

convolution In mathematics (in particular, functional analysis), convolution is a operation (mathematics), mathematical operation on two function (mathematics), functions f and g that produces a third function f*g, as the integral of the product of the two ...

of a

negative binomial distribution In probability theory and statistics, the negative binomial distribution, also called a Pascal distribution, is a discrete probability distribution that models the number of failures in a sequence of independent and identically distributed Berno ...

with a

Poisson distribution In probability theory and statistics, the Poisson distribution () is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time if these events occur with a known const ...

. Just as the

can be viewed as a Poisson distribution where the mean parameter is itself a random variable with a

gamma distribution In probability theory and statistics, the gamma distribution is a versatile two-parameter family of continuous probability distributions. The exponential distribution, Erlang distribution, and chi-squared distribution are special cases of the g ...

, the Delaporte distribution can be viewed as a

compound distribution In probability and statistics, a compound probability distribution (also known as a mixture distribution or contagious distribution) is the probability distribution that results from assuming that a random variable is distributed according to some ...

based on a Poisson distribution, where there are two components to the mean parameter: a fixed component, which has the

\lambda

parameter, and a gamma-distributed variable component, which has the

\alpha

and

\beta

parameters. The distribution is named for Pierre Delaporte, who analyzed it in relation to automobile accident claim counts in 1959, although it appeared in a different form as early as 1934 in a paper by Rolf von Lüders, where it was called the Formel II distribution.

Properties

The

skewness In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. The skewness value can be positive, zero, negative, or undefined. For a unimodal ...

of the Delaporte distribution is:

\frac

The

excess kurtosis In probability theory and statistics, kurtosis (from , ''kyrtos'' or ''kurtos'', meaning "curved, arching") refers to the degree of “tailedness” in the probability distribution of a real-valued random variable. Similar to skewness, kurtosi ...

of the distribution is:

\frac

References

External links

{{DEFAULTSORT:Delaporte distribution Discrete distributions Compound probability distributions

Properties

References

Further reading

External links