On Quasi-Weibull Distribution

Abstract

Exponential distribution together with a variety of its transformations is permanently used both in probability theory and related fields. The most popular one is the power transformation yielding the Weibull distribution. In this paper, the power distribution of exponential random variable is supplemented by a logarithmic factor leading to a new distribution called quasi-Weibull. This is a three-parameter distribution, where one parameter is inherited from the underlying exponential distribution, and the others originate from the transformation. The properties of the quasi-Weibull distribution are studied. Specifically, the impact of the parameters on the analyticity of characteristic function, the existence of the moment generating function, the moment-determinacy/indeterminacy and the behaviour of the hazard function are investigated.