On a class of inverted distributions

Abstract

The probability distributions corresponding to the reciprocal transformations arise in different statistical and scientific works, for example in problems related to econometrics, biological sciences, survey sampling, engineering sciences and life testing problems. Some authors have recently attempted to study the moments of the inverted class of certain distributions which can also be interpreted as negative moments of the distributions. In this thesis an attempt is made to generate a new class of inverted distributions using a unified approach of transformation and to generalize Pearsonian class of distributions. Various mathematical and statistical properties of the inverted distributions are discussed and some mathematical characterizations are obtained. The hazard functions of the inverted class of distributions, unlike their parent distributions, are shown to have an analogy with the hazard functions of the logarithmic normal and Bernstein distributions. This unique feature of hazard functions suggests the applicability of inverted distributions in medicine sciences, i.e., analytical study of disease control, mortality studies and life testing.