Kaniadakis Erlang distribution


The Kaniadakis Erlang distribution is a family of continuous statistical distributions, which is a particular case of the κ-Gamma distribution, when and positive integer. The first member of this family is the κ-exponential distribution of Type I. The κ-Erlang is a κ-deformed version of the Erlang distribution. It is one example of a Kaniadakis distribution.

Characterization

Probability density function

The Kaniadakis κ-Erlang distribution has the following probability density function:
valid for and, where is the entropic index associated with the Kaniadakis entropy.
The ordinary Erlang Distribution is recovered as.

Cumulative distribution function

The cumulative distribution function of κ-Erlang distribution assumes the form:
valid for, where. The cumulative Erlang distribution is recovered in the classical limit.

Survival distribution and hazard functions

The survival function of the κ-Erlang distribution is given by:
The survival function of the κ-Erlang distribution enables the determination of hazard functions in closed form through the solution of the κ-rate equation:
where is the hazard function.

Family distribution

A family of κ-distributions arises from the κ-Erlang distribution, each associated with a specific value of, valid for and. Such members are determined from the κ-Erlang cumulative distribution, which can be rewritten as:
where
with

First member

The first member of the κ-Erlang family is the κ-Exponential distribution of type I, in which the probability density function and the cumulative distribution function are defined as:

Second member

The second member of the κ-Erlang family has the probability density function and the cumulative distribution function defined as:

Third member

The second member has the probability density function and the cumulative distribution function defined as:

Related distributions