Characterizations of Some Probability Distributions with Completely Monotonic Density Functions

For a non-negative continuous random variable , Chaudhry and Zubair (2002, p. 19) introduced a probability distribution with a completely monotonic probability density function based on the generalized gamma function, and called it the Macdonald probability function. In this paper, we establish vari...

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Bibliographic Details
Published in:Pakistan journal of statistics and operation research Vol. 17; no. 1; pp. 51 - 64
Main Authors: Shakil, Mohammad, Dr. Mohammad Ahsanullah, Kibria, Dr. B. M. G. Kibria
Format: Journal Article
Language:English
Published: Lahore University of the Punjab, College of Statistical & Actuarial Science 02.03.2021
Subjects:
Continuity (mathematics)
Gamma function
Probability density functions
Probability distribution
Random variables
Statistical analysis
ISSN:1816-2711, 2220-5810
Online Access:Get full text
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Summary:For a non-negative continuous random variable , Chaudhry and Zubair (2002, p. 19) introduced a probability distribution with a completely monotonic probability density function based on the generalized gamma function, and called it the Macdonald probability function. In this paper, we establish various basic distributional properties of Chaudhry and Zubair’s Macdonald probability distribution. Since the percentage points of a given distribution are important for any statistical applications, we have also computed the percentage points for different values of the parameter involved. Based on these properties, we establish some new characterization results of Chaudhry and Zubair’s Macdonald probability distribution by the left and right truncated moments, order statistics and record values. Characterizations of certain other continuous probability distributions with completely monotonic probability density functions such as Mckay, Pareto and exponential distributions are also discussed by the proposed characterization techniques.   
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ISSN:1816-2711
2220-5810
DOI:10.18187/pjsor.v17i1.3491