The negative binomial distribution has become increasingly popular as a more flexible alternative to Poisson distribution, especially when it is questionable whether the strict requirements for Poisson distribution could be satisfied. But negative binomial distribution is better for overdispersed count data that are not necessarily heavy-tailed, for heavy tailed count data the traditional stati...

In this paper, a generalized version of the inverted exponential distribution called the weighted inverted exponential distribution is introduced. The proposed distribution is used to analyze lifetime data. Several statistical properties of the weighted inverted exponential distribution are studied and derived. Least squares estimation, maximum likelihood estimation and Bayesian estimation meth...

From the integration of nonsymmetrical hyperboles, a one-parameter generalization of the logarithmic function is obtained. Inverting this function, one obtains the generalized exponential function. Motivated by the mathematical curiosity, we show that these generalized functions are suitable to generalize some probability density functions pdfs . A very reliable rank distribution can be conveni...