Ordinary differential equations of the probability functions of the Benktander kind II distribution with b = 1 and its properties
The idea of convolution is the sum of independent and identically distributed
(iid) random variables and the structure of linear combination of random variables.
The cases of ordinary differential equation (ODE) of the convolution of probability
distributions of mixture of Benktander distribution of the second kind have been
studied. Moreover, the ODE of quantile function (QF), survival function (SF), hazard
function (HF) and reversed hazard function (RHF) of convoluted probability distributions
has been considered. We obtain explicit forms for the densities and distribution
functions for Benktander distribution of the second kind, as well as their moments
and related parame-ters. We derive basic properties of these laws and illustrate their
modeling possible using a simulated data.