The Kumaraswamy compound Rayleigh distribution : properties and estimation
Keywords:Kumaraswamy Distribution, Compound Rayleigh Distribution, Order Statistics, Record Statistics, Moments Estimation, Maximum Likelihood Estimation.
We introduce a new four parameter continuous model, called the Kumaraswamy compound Rayleigh (KwCR) distribution that extends the compound Rayleigh distribution. We study some mathematical properties of this distribution such as; mean, variance, coefficient of variation, quantile function, median, ordinary and incomplete moments, skewness, kurtosis, moment and probability generating functions, reliability analysis, Lorenz, Bonferroni and Zenga curves, RÃ©nyi of entropy, order statistics and record statistics. We consider the methods of moments and maximum likelihood for estimating the model parameters.
 T.A. Abushal, Estimation of the unknown parameters for the compound Rayleigh distribution based on progressive first-failure-censored sampling, Open Journal of Statistics, 1 (2011) 161-171. https://doi.org/10.4236/ojs.2011.13020.
 O. Shajaee, R. Azimi and M. Babanezhad, Empirical Bayes estimators of parameter and reliability function for compound Rayleigh distribution under record data, American Journal of Theoretical and Applied Statistics, 1 (2012) 12-15. https://doi.org/10.11648/j.ajtas.20120101.12.
 D.R. Barot, and M.N. Patal, Performance of estimates of reliability parameters for compound Rayleigh progressive type-ii censored data, Control Theory and Informatics, 5 (2015) 33-41.
 G.A. Abd-Elmougod, and E.E. Mahmoud, Parameters estimation of compound Ratleigh distribution under an adaptive type-ii progressive hybrid censored data for constant partially accelerated life tests. Global Journal of Pure and Applied Mathematics, 12(2016) 3253-3273.
 G.M. Cordeiro and M. de Castro, A new family of generalized distributions, Journal of Statistical Computation and Simulation, (2009) 1-17.
 B.O. Oluyede, and S. Rajasooriya, The Mc-Dagum distribution and its statistical properties with applications, Asian Journal of Mathematics and Applications, 44 (2013) 1-16.
 M. Ahsanullah, Record Statistics, New York: Nova Science Publishers, Inc. Commack.1995.
 B.C. Arnold, N. Balakrishan, and H.N. Nagaraja, Records. New York: Wiley, USA.1998.