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Characterization of Probability Distributions
Engels
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Characterization results have great importance in statistics and probability applications. The concept of failure rate, mean residual life, reversed failure rate and mean inactivity time, also known as reversed mean residual life, are extensively used in modeling and analysis in reliability studies and applicable in other disciplines such as economics, biostatistics, actuarial sciences, engineering, biology, biometry and applied probability areas. This book provides two new characterizations of gamma distribution by establishing a connection between s-right truncated moments (s-left truncated moments) and reversed hazard rate (hazard rate). Also it provides new characterizations of Exponential, Power Function, Pareto of the first kind and Pareto of the second kind distributions are presented by using s- conditional expectation of order statistics in terms of their failure (hazard) rate. These characterization results are easier to check in data analysis. Besides, our results generalize some of the known results. A Simulation study showed that all the characterization results give an easy way for the practitioner to test whether the available data follows a particular distribut
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