DOI QR코드

DOI QR Code

On Distribution of Order Statistics from Kumaraswamy Distribution

Garg, Mridula

  • Received : 2007.02.16
  • Published : 2008.09.30

Abstract

In the present paper we derive the distribution of single order statistics, joint distribution of two order statistics and the distribution of product and quotient of two order statistics when the independent random variables are from continuous Kumaraswamy distribution. In particular the distribution of product and quotient of extreme order statistics and consecutive order statistics have also been obtained. The method used is based on Mellin transform and its inverse.

Keywords

Fox H function;Kumaraswamy distribution;Mellin transform;order statistics;random variable

References

  1. A. Erdelyi et. al., Table of Integral Transforms, Vol. I, McGraw-Hill, New York, Toronto and London, 1954.
  2. C. Fox, Some applications of Mellin transforms to the theory of bivariate statistical distribution, Proc. Cambridge Philos. Soc., 53(1957), 620-628. https://doi.org/10.1017/S0305004100032679
  3. E. J. Gumble, Statistics of Extremes, Columbia University Press, New York, London, 1960.
  4. E. J. Gumble and L. H. Herbach,The exact distribution of the extremal quotient, Annals of Mathematical Statistics, 22(1951), 418-126. https://doi.org/10.1214/aoms/1177729588
  5. H. A. David, Order Statistics, John Wiley & Sons, New York, 1970.
  6. H. Malik and R. Trudel, Distribution of product and quotient of order statistics, University of Guelph Statistical Series, 1975-30(1976), 1-25.
  7. H. M. Srivastava, K. C. Gupta and S. P. Goyal, The H-function of One and Two Variables with Applications, South Asian Publishers, New Delhi and Madras, 1982.
  8. J. D. Gibbons, Non Parametric Statistical Inference, Mc Graw Hill, Koyakusha, Ltd., Tokyo, 1971.
  9. K. Subrahmanian, On some applications of Mellin transform to statistics : Dependent random variables, SIAM Journal of Applied Mathematics, 19(1970), 658-662. https://doi.org/10.1137/0119064
  10. M. D. Springer, The Algebra of Random Variables, John Wiley & Sons, New York, 1979.
  11. P. Kumaraswamy, A generalized probability density function for double-bounded random process, Journal of Hydrology, 46(1980), 79-88. https://doi.org/10.1016/0022-1694(80)90036-0

Cited by

  1. New Properties of the Kumaraswamy Distribution vol.42, pp.5, 2013, https://doi.org/10.1080/03610926.2011.581782
  2. The Kumaraswamy distribution: median-dispersion re-parameterizations for regression modeling and simulation-based estimation vol.54, pp.1, 2013, https://doi.org/10.1007/s00362-011-0417-y
  3. Estimation of reliability of multicomponent stress–strength for a Kumaraswamy distribution vol.46, pp.4, 2017, https://doi.org/10.1080/03610926.2015.1022457
  4. Estimating the Parameters of Kumaraswamy Distribution Using Progressively Censored Data vol.47, pp.2, 2018, https://doi.org/10.1520/JTE20150393