Existence conditions and properties for the generalized Euler family of distributions
The paper investigates a generalized Euler family of distributions and obtains the following significant results: (1) Existence conditions for the probability mass function and the probability generating function of the corresponding generalized Euler family of distributions. (2) Identification of the obtained conditions with those corresponding to various distributions already existing in the literature. (3) For the considered class of distributions, the author examines several important properties using the methods enclosed in the valuable approach of \textit{P. L. Gupta}, \textit{R. C. Gupta} and \textit{R. C. Tripathi} [ibid. 65, No. 2, 255-268 (1997; Zbl 0908.62099)], showing that these properties depend greatly on the parameter constraints: logconcavity, logconvexity, failure rate behaviour, infinite divisibility, strong unimodality, over- and underdispersion.
scientific article; zbMATH DE number 1741597
scientific article