A New Distribution and Application on the Lifetime Data

Authors: Gamze Ozel, Selen Cakmakyapan

Abstract:

We introduce a new model called the Marshall-Olkin Rayleigh distribution which extends the Rayleigh distribution using Marshall-Olkin transformation and has increasing and decreasing shapes for the hazard rate function. Various structural properties of the new distribution are derived including explicit expressions for the moments, generating and quantile function, some entropy measures, and order statistics are presented. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. The potentiality of the new model is illustrated by means of a simulation study. 

Keywords: Marshall-Olkin distribution, Rayleigh distribution, estimation, maximum likelihood.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1109099

References:

[1] L. Rayleigh, “On the stability or instability of certain fluid motions”, in Proc. of the London Mathematical Society, vol. 11, 1880, pp. 57-70.
[2] V.G. Vodà, “Note on the truncated Rayleigh variate”, Revista Colombiana de Matemáticas, vol. 9, 1975, pp. 1–7.
[3] J. Leao, H. Saulo, M. Bourguignon, R. Cintra, L. Rego, and G. Cordeiro, “On some properties of the beta inverse Rayleigh distribution”, Chilean Journal of Statistics, vol. 4, 2013, pp. 111–131.
[4] A. Ahmad, S.P. Ahmad, and A. Ahmed, “Transmuted inverse Rayleigh distribution: A generalization of the inverse Rayleigh distribution”, Mathematical Theory and Modeling, vol. 4, 2014, pp. 90-98.
[5] A.W. Marshall and I. Olkin, “A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families”, Biometrika, vol. 84, 1997, pp. 641-652.
[6] A. Rényi, “On measures of entropy and information”. in Proc. of the 4th Berkeley Symposium, 1961.
[7] C.E. Shannon, “Prediction and entropy of printed English”. Bell System Technical Journal, vol. 30, 1951, pp. 50-64.