Abdus Saboor

The moment generating function of a bivariate gamma-type distribution

A bivariate gamma-type density function involving a confluent hypergeometric function of two variables is being introduced. The inverse Mellin transform technique is employed in conjunction with the transformation of variable technique to obtain its moment generating function, which is expressed in terms of generalized hypergeometric functions. Its cumulative distribution function is given in closed form as well. Many distributions such as the bivariate Weibull, Rayleigh, half-normal and Maxwell distributions can be obtained as limiting cases of the proposed gamma-type density function. Computable representations of the moment generating functions of these distributions are also provided.

Marshall–Olkin gamma–Weibull distribution with applications

Abstract A Marshall–Olkin variant of the Provost type gamma–Weibull probability distribution is being introduced in this paper. Some of its statistical functions and numerical characteristics among others characteristics function, moment generalizing function, central moments of real order are derived in the computational series expansion form and various illustrative special cases are discussed. This density function is utilized to model two real data sets. The new distribution provides a better fit than related distributions as measured by the Anderson–Darling and Cramér–von Mises statistics. The proposed distribution could find applications for instance in the physical and biological sciences, hydrology, medicine, meteorology, engineering, etc.

The Marshall-Olkin exponential Weibull distribution

A new four-parameter model called the Marshall‐Olkin exponential‐ Weibull probability distribution is being introduced in this paper, generalizing a number of known lifetime distributions. This model turns out to be quite flexible for analyzing positive data. The hazard rate functions of the new model can be increasing and bathtub shaped. Our main objectives are to obtain representations of certain associated statistical functions, to estimate the parameters of the proposed distribution and to discuss its modality. As an application, the probability density function is utilized to model two actual data sets. The new distribution is shown to provide a better fit than related distributions as measured by the Anderson‐Darling and Cramer‐von Mises goodness‐ of‐fit statistics. The proposed distribution may serve as a viable alternative to other distributions available in the literature for modeling positive data arising in various fields of scientific investigation such as reliability theory, hydrology, medicine, meteorology, survival analysis and engineering.

The Transmuted Exponentiated Weibull Geometric Distribution: Theory and Applications

A generalization of the exponentiated Weibull geometric model called the transmuted exponentiated Weibull geometric distribution is proposed and studied. It includes as special cases at least ten models. Some of its structural properties including order statistics, explicit expressions for the ordinary and incomplete moments and generating function are derived. The estimation of the model parameters is performed by the maximum likelihood method. The use of the new lifetime distribution is illustrated with an example. We hope that the proposed distribution will serve as a good alternative to other models available in the literature for modeling positive real data in several areas.

Corrigendum to ‘some gamma distributions’ by Saralees Nadarajah

In ‘Some Gamma Distributions’ published in Statistics: A Journal of Theoretical and Applied Statistics, 2008;42(1):77–94 (http://dx.doi.org/10.1080/02331880701529621), the second author introduced a new generalized gamma probability density function (named as generalized gamma distribution) in the following form: f (x) = Cxα−1(x + z)−ρ exp (−λx) (1) for x > 0, α > 0, λ > 0, z > 0, and −∞ < ρ < ∞, where C = C(α, λ, z, ρ) denotes a normalizing constant defined by 1 C(α, λ, z, ρ) = zα−ρ (α) (α, α + 1 − ρ; λz) (2)