Expectation Properties of Generalized Order Statistics from Poisson Lomax Distribution
Abstract
The Poisson Lomax distribution was proposed by [3], as a useful model for analyzing lifetime data. In this paper,we have derived recurrence relations for single and product moments of generalized order statistics for this distribution. Further, characterization of the distribution is carried out. Some deductions and particular cases are also discussed.References
M. A. Ali, and A. H. Khan, Recurrence relations for the expectations of a function of single order statistic from general class of distributions, Journal of Indian Statistical Association, vol. 35, pp. 1-9, 1997.
M. A. Ali, and A. H. Khan, Recurrence relations for the expected values of certain functions of two order statistic, Metron, vol. 56, no. 1-2, pp. 1-9, 1998.
B. Al-Zahranii, and H. Sagor, The Poisson-Lomax distribution, Revista Colombiana de Estadistica, vol. 37, no. 1, pp. 223-243,2014.
Z. Anwar, H. Athar and R. U. Khan, Expectation identities based on recurrence relations of functions of generalized order statistics, Journal of Statistical Research, vol. 41, pp. 93-102, 2008.
B. C. Arnold, N. Balakrishnan and H. N. Nagaraja, A First Course in Order Statistics, John Wiley, New York., 1992.
H. Athar, and Z. Akhter, Some characterizations of continuous distributions based on order statistics, International Journal of Computational and Theoretical Statistics, vol. 2, no. 1, pp. 31-36, 2015.
H. Athar, and H. M. Islam, Recurrence relations for single and product moments of generalized order statistics from a general class of distributions, Metron., vol. 62, no. 3, pp. 327-337, 2004.
H. Athar, S. K. Khwaja and Nayabuddin, Expectation identities of Pareto distributions based on generalized order statistics and its characterization, American Journal of Applied Mathematics and Mathematical Sciences, vol. 1, no. 1, pp. 23-29, 2012.
H. Athar and Z. Noor, Characterization of probability distributions through conditional expectation of function of pair of order statistics, Journal of Applied Probability and Statistics, vol. 8, no. 1, pp. 45-56, 2013.
H. Athar and Y. A. Aty, Characterization of general class of distribution by truncated moment, Thailand Statistician, vol. 18, no.2, in press, 2020.
H. Athar, M. Yaqub and H. M. Islam, On characterizations of distributions through linear regression of record values and order statistics, Aligarh Journal of Statistics, vol. 23, 97-105, 2003.
N. Balakrishnan, H. J. Malik and S. E. Ahmed, Recurrence relations and identities of moments of order statistics, II: Specific continuous distributions, Communications in Statistics-Theory and Methods, vol. 17, no. 8, 2657-2694, 1988.
J. Galambos and S. Kotz, Characterizations of Probability Distributions, Springer, New York, 1978.
I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series and Products, Edited by Jeffrey, A. and Zwillinger, D. 7th Ed., Academic Press, New York, 2007.
N. Gupta and Z. Anwar, Relations for Single and Product Moments of Odds Generalized Exponential-Pareto Distribution Based on Generalized Order Statistics and Characterization , Statistics, Optimization and Information Computing, vol.7, no.1,160-170, 2019.
J. S. Hwang and G. D. Lin, Extentions of Muntz-Szasz theorems and applications, Analysis, vol. 4, 143-160, 1984.
U. Kamps, A Concept of Generalized Order Statistics, B.G. Tuebner Stuttgart, Germany, 1995.
U. Kamps and E. Cramer, On distribution of generalized order statistics, Statistics, vol. 35, no. 3, 269-280, 2001.
C. Keseling, Conditional distributions of generalized order statistics and some characterizations, Metrika, vol. 49, 27-40, 1999.
A. H. Khan and A. M. Abouammoh, Characterization of distributions by conditional expectation of order statistics, Journal of Applied Statistics and Science, vol. 13, no. 2, 159-167, 2000.
A. H. Khan and A. A. Alzaid, Characterization of distributions by conditional expectation of order statistics, Journal of Applied Statistics and Science, vol. 13,123-136, 2004.
A. H. Khan and H. Athar, Characterization of distributions through order statistics, Journal of Applied Statistics and Science, vol. 13, no. 2, 159-167, 2004.
A. H. Khan, R. U. Khan and M. Yaqub, Characterization of continuous distributions through conditional expectation of function of generalized order statistics, Journal of Applied Probability and Statistics, vol. 1, no. 1, 115-131, 2006.
A. H. Khan, S. Parvez and M. Yaqub, Recurrence relations between product moments of order statistics, Journal of Statisticsn Planning and Inference, vol. 8, 175-183, 1983.
A. H. Khan, S. Parvez and M. Yaqub, Recurrence relations between moments of order statistics, Naval Research Logistics Quarterly, vol. 30, no. 3, 419-441, 1983.
R. U. Khan, M. A. Khan and M. A. R. Khan, Relations for moments of generalized record values from additive Weibull distribution and associated inference, Statistics, Optimization and Information Computing, vol. 5, no. 2, 127-136, 2017.
R. U. Khan, D. Kumar and H. Athar, Moments of generalized order statistics from Erlang-truncated exponential distribution and its characterization, International Journal of Statistics and Systems, vol. 5, no. 4, 455-464, 2010.
S. Kotz and D. N. Shanbhag, Some new approaches to probability distributions, Advances in Applied Probability, vol. 12, no. 4, 455-464, 1980.
H. J. Malik, N. Balakrishnan and S. E. Ahmed, Recurrence relations and identities of moments of order statistics, I: Arbitrary continuous distributions, Communications in Statistics - Theory and Methods, vol. 17, 2623-7826, 1988.
Nayabuddin and H. Athar, Recurrence relations for single and product moments of generalized order statistics from Marshall-Olkin extended Pareto distribution, Communications in Statistics - Theory and Methods, vol. 46, no. 16, 7820-7826, 2017.
P. Pawlas and D. Szynal, Recurrence relations for single and product moments of generalized order statistics from Pareto, Generalized Pareto and Burr distributions, Communications in Statistics - Theory and Methods, vol. 30, no. 4, 739-746, 2001.
B. Singh, R. U. Khan and M. A. R. Khan, Generalized order statistics from Kumaraswamy-Burr III distribution and related inference, Journal of Statistics: Advances in Theory and Applications, vol. 19, no. 1, 1-16, 2018.
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