Karim, Rezaul; Hossain, Pear; Begum, Sultana; Hossain, Forhad Rayleigh mixture distribution. (English) Zbl 1235.62016 J. Appl. Math. 2011, Article ID 238290, 17 p. (2011). Summary: This paper presents Rayleigh mixtures of distributions in which the weight functions are assumed to be chi-square, \(t\) and \(F\) sampling distributions. The exact probability density functions of the mixture of two correlated Rayleigh random variables have been derived. Different moments, characteristic functions, shape characteristics, and estimates of the parameters of the proposed mixture distributions using the method of moments have also been provided. Cited in 2 Documents MSC: 62E15 Exact distribution theory in statistics 62F10 Point estimation PDF BibTeX XML Cite \textit{R. Karim} et al., J. Appl. Math. 2011, Article ID 238290, 17 p. (2011; Zbl 1235.62016) Full Text: DOI OpenURL References: [1] K. Pearson, “Contribution to the mathematical theory of evolution,” Philosophical Transactions of the Royal Society A, vol. 185, pp. 71-110, 1894. · JFM 25.0347.02 [2] W. Mendenhall and R. J. Hader, “Estimation of parameters of mixed exponentially distributed failure time distributions from censored life test data,” Biometrika, vol. 45, pp. 504-520, 1958. · Zbl 0088.12302 [3] V. Hasselblad, “Estimation of mixtures of distribution from the exponential family,” Journal of American Statistical Association, vol. 64, no. 328, pp. 300-314, 1968. [4] H. E. Daniels, “Mixtures of geometric distributions,” Journal of the Royal Statistical Society: Series B, vol. 23, pp. 409-413, 1961. · Zbl 0161.15601 [5] J. Chaine, “Une generalization dela loi binomiale negative,” Revue de Statistique Appliqué, vol. 13, no. 4, pp. 33-43, 1965. [6] M. K. Roy, S. Rahman, and M. M. Ali, “A class of poisson mixtured distributions,” Journal of Information & Optimization Sciences, vol. 13, no. 2, pp. 207-218, 1992. · Zbl 0758.62013 [7] M. K. Roy, A. K. Sen, and M. M. Ali, “Binomial mixture of some distributions,” Journal of Information & Optimization Sciences, vol. 13, no. 2, pp. 207-218, 1993. [8] M. K. Roy and S. K. Sinha, “Negative binomial mixture of normal moment distributions,” Metron, vol. 53, no. 3-4, pp. 83-91, 1995. · Zbl 0860.62014 [9] M. K. Roy and S. K. Sinha, “Negative binomial mixture of chi-square and F- distributions,” Journal of Bangladesh Academy of Statistical Sciences, vol. 21, no. 1, pp. 25-34, 1997. [10] M. K. Roy, M. F. Imam, and J. C. Paul, “Gamma mixture of normal moment distribution,” International Journal of Statistical Sciences, vol. 1, pp. 20-24, 2002. [11] M. K. Roy, M. R. Zaman, and N. Akter, “Chi-square mixture of gamma distribution,” Journal of Applied Sciences, vol. 5, no. 9, pp. 1632-1635, 2005. [12] M. K. Roy, M. E. Haque, and B. C. Paul, “Earlang mixture of normal moment distribution,” International Journal of Statistical Sciences, vol. 6, pp. 29-37, 2007. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.