SOME INFERENCES ON OFFSET NORMAL DISTRIBUTION: PROPERTIES AND CHARACTERIZATIONS
M. Ahsanullah, M. Shakil and Ahmed M. T. Abd El-Bar
Professor Emeritus, Department of Management Sciences, Rider University, Lawrenceville, NJ 08648, USA
Department of Mathematics, Liberal Arts and Sciences, Miami Dade College, Hialeah, FL 33024, USA
Department of Mathematics, Faculty of Science, Tanta University, Tanta 31527, Egypt
Email:email@example.com, firstname.lastname@example.org, email@example.com
(Received : August 15,2021 ; In format : August 25, 2021 ; Revised in final form : September 26,2021)
The offset normal distribution, defined as the induced shape parameter of a Gaussian random configuration in the plane, is one of the most important probability distributions with tremendous applications both in pure and applied mathematics. In this paper some basic properties of the offset normal distribution are discussed. Based on the basic properties, several characterizations are presented by the left and right truncated moments. The first characterization result is based on a relation between left truncated moment and failure rate function. The second characterization result is based on a relation between right truncated moment and reversed failure rate function.
2020 Mathematical Sciences Classification: 60E05, 62E10, 62E15, 62G30.
Keywords and Phrases: Offset normal distribution, Moments, Shannon entropy, Truncated moments, Characterization
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