On a Generalisation of Uniform Distribution and its Properties
DOI:
https://doi.org/10.6092/issn.1973-2201/6090Keywords:
Distribution of order statistics, Entropy, Marshall-Olkin family of distributions, Maximum likelihood, Random variate generation, Truncated negative binomial distributionAbstract
Nadarajah et al.(2013) introduced a family life time models using truncated negative binomial distribution and derived some properties of the family of distributions. It is a generalization of Marshall-Olkin family of distributions. In this paper, we introduce Generalized Uniform Distribution (GUD) using the approach of Nadarajah et al.(2013). The shape properties of density function and hazard function are discussed. The expression for moments, order statistics, entropies are obtained. Estimation procedure is also discussed.The GDU introduced here is a generalization of the Marshall-Olkin extended uniform distribution studied in Jose and Krishna(2011).
References
K. JAYAKUMAR, M. THOMAS (2008). On a generalization to Marshall-Olkin scheme and its application to Burr type XII distribution. Statist. Pap., 49, 421-439.
K. K. JOSE, E. KRISHNA (2011). Marshall-Olkin extended uniform distribution. ProbStat Forum, 04, 78-88.
A. W. MARSHALL, I. OLKIN (1997). A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families. Biometrika, 84, 641-652.
S. NADARAJAH, K. JAYAKUMAR, M. M. RISTIC (2013). A new family of lifetime models. Journal of Statistical Computation and Simulaion, 83, 1389-1404.
A. P. PRUDNIKOV, Y. A. BRYCHKOV, O. I. MARICHEV (1986). Integrals and series vol. I. Gordeon and Breach Sciences, Amsterdam, Netherlands.
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