Continuous probability distributions are widely used to mathematically describe random phenomena in engineering and physical sciences. In this paper, we present a methodology that can be used to formalize any continuous random variable for which the inverse of the cumulative distribution function can be expressed in a closed mathematical form. Our methodology is primarily based on the Standard ...

The distribution of ratio of two random variables has been studied by several authors especially when the two random variables are independent and come from the same family. In this paper, the exact distribution of the ratio of two independent HyperErlang distribution is derived. However, closed expressions of the probability density, cumulative distribution function, reliability function, haza...

In this paper, we consider a form of the generalized logistic distribution named symmetric extended generalized logistic distribution or extended type III generalized logistic distribution. The distribution is derived by compounding a two-parameter generalized Gumbel distribution with a two-parameter generalized gamma distribution. The cumulative distribution and some properties of this distrib...

Abstract A procedure is presented for using the bivariate normal distribution to describe the joint distribution of storm peaks (maximum rainfall intensities) and amounts which are mutually correlated. The Box-Cox transformation method is used to normalize original marginal distributions of storm peaks and amounts regardless of the original forms of these distributions. The transformation param...

This article develops a beta-exponentiated Ishita distribution that extends the exponentiated Ishita distribution. Expansions for cumulative and probability density functions are given. Various properties of new such as hazard function, moments, cumulants, skewness, kurtosis, mean deviations, Bonferroni Lorenz curves, Renyi Tsallis entropies, stress-strength reliability discussed. Moment ...