Stochastic Comparison of Hariss Family Distributions with Fixed and Randomized tilt Parameter

Abbasi, Somayeh; Alamatsaz, Mohammad Hossein

doi:10.22034/jirss.2022.707183

Stochastic Comparison of Hariss Family Distributions with Fixed and Randomized tilt Parameter

Document Type : Original Article

Authors

Somayeh Abbasi ¹

Mohammad Hossein Alamatsaz ²

¹ Department of Mathematics, Isfahan (Khorasgan) Branch, Islamic Azad University, Isfahan,Iran

² Department of Statistics, University of Isfahan, Isfahan, Iran

10.22034/jirss.2022.707183

Abstract

In this paper, we stochastically compare Harris family distributions having random tilt parameter with Harris family distributions having fixed tilt parameter. We also study certain preservation properties of mixtures of Harris family of distributions with regards to their baseline distributions. Comparison tools are various types of orderings, such as the usual, shifted, proportional and shifted proportional stochastic orderings. Several previous findings, regarding Marshall-Olkin family, follow as special cases of our results. We shall also fit a new Harris model to a real data set to illustrate the usefulness of our comparisons.

Keywords

Marshall-Olkin Distribution

Proportional Stochastic Ordering

Shifted Stochastic Ordering

Shifted Proportional Stochastic Ordering

Usual Stochastic Ordering

Reliability Function

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