Moment Properties of Generalized Order Statistics From Lindley Pareto Distribution
Keywords:
Lindley Pareto distribution, single moment, product moments, recurrence relation, order statistics, record value, generalized order statistics and characterization.
Abstract
The Lindley Pareto distribution is a more flexible model for analyzing the lifetime data. In this paper, moment properties of generalized order statistics from Lindley Pareto distribution in terms of exact expression and recurrence relations are studied. The results for order statistics, record values, and progressive type II right censored order statistics are discussed as particular cases of generalized order statistics. Further, the characterizations of the said distribution through recurrence relations between moments of generalized order statistics are presented.References
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generalized order statistics. Journal of Statistical Planning and Inference, 89(1-2),
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generating functions of generalized order statistics from power function distribution.
Metron, 61(1), 27-33.
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moments of generalized order statistics from doubly truncated distributions. Journal
of statistical planning and inference, 117(2), 241-249.
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linear exponential distribution and a characterization. Journal of Applied Probability
and Statistics, 9(1), 53-65.
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Marshall-Olkin extended exponential distribution. Journal of Statistical Theory and
Applications, 18(2), 129-135.
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Order Statistics from Exponentiated Generalized Class of Distributions. Thailand
Statistician, 19(4), 797-811.
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generalized order statistics from Poisson Lomax distribution. Statistics, Optimization
and Information Computing, 9(3), 735-747.
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Order Statistics Based on Modified Weighted Rayleigh Distribution. European
Journal of Statistics, 3, 1-1.
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distributions through conditional expectation of functions of generalized order
statistics. J. Appl. Probab. Statist, 1, 115-131.
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distributions through conditional expectation of generalized and dual generalized
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order statistics and characterization of probability distributions. J. Stat. Appl. Pro.
Lett, 1(1), 9-18.
[29] Athar, H. and Abdel-Aty, Y. (2020). Characterization of general class of distributions
by truncated moment. Thailand Statistician, 18(2), 95-107.
[30] Ahsanullah, M., Ghitany, M. E. and Al-Mutairi, D. K. (2017). Characterization of
Lindley distribution by truncated moments. Communications in Statistics-Theory
and Methods, 46(12), 6222-6227.
[31] Glanzel, W. (1990). Some consequences of a characterization theorem based on
truncated moments. Statistics, 21(4), 613-618.
[32] Kotz, S. and Shanbhag, D. N. (1980). Some new approaches to probability
distributions. Advances in Applied Probability, 12(4), 903-921.
[33] Gradshteyn, I. S. and Ryzhik, I. M. (2014). Table of integrals, series, and products.
Academic press.
[34] Akhter, Z., MirMostafaee, S. M. T. K. and Ormoz, E. (2022). On the order statistics
of exponentiated moment exponential distribution and associated inference. Journal
of Statistical Computation and Simulation, 92(6), 1322-1346.
[35] Akhter, Z., Saran, J., Verma, K. and Pushkarna, N. (2020). Moments of order
statistics from length-biased exponential distribution and associated inference.
Annals of Data Science, 1-26.
[36] David, H. A. and Nagaraja, H. N. (2004). Order statistics. John Wiley and Sons.
Statistics, 671.
[2] Athar, H. and Islam, H. M. U. (2004). Recurrence relations for single and product
moments of generalized order statistics from a general class of distribution. Metron-
International Journal of Statistics, 62(3), 327-337.
[3] Kamps, U. (1995). A concept of generalized order statistics. Journal of Statistical
Planning and Inference, 48(1), 1-23.
[4] Kamps, U. and Cramer, E. (2001). On distributions of generalized order statistics.
Statistics, 35(3), 269-280.
[5] Lindley, D. V. (1958). Fiducial distributions and Bayes’ theorem. Journal of the Royal
Statistical Society. Series B (Methodological), 102-107..
[6] Pawlas, P. and Szynal, D. (2001). Recurrence relations for single and product
moments of generalized order statistics from Pareto, generalized Pareto, and Burr
distributions. Communications in Statistics-theory and Methods, 30(4), 739-746.
[7] Pawlas, P. and Szynal, D. (2001). Recurrence relations for single and product
moments of lower generalized order statistics from the inverse Weibull distribution.
Demonstratio Mathematica, 34(2), 141-146.
[8] Cramer, E. and Kamps, U. (2000). Relations for expectations of functions of
generalized order statistics. Journal of Statistical Planning and Inference, 89(1-2),
79-89.
[9] Keseling, C. (1999). Conditional distributions of generalized order statistics and some
characterizations. Metrika, 49, 27-40.
[10] Saran, J. and Pandey A. (2003). Recurrence relations for marginal and joint moment
generating functions of generalized order statistics from power function distribution.
Metron, 61(1), 27-33.
[11] Ahmad, A. E. B. A. and Fawzy, M. A. (2003). Recurrence relations for single
moments of generalized order statistics from doubly truncated distributions. Journal
of statistical planning and inference, 117(2), 241-249.
[12] Khan, R. U. and Zia, B. E. (2014). Generalized order statistics of doubly truncated
linear exponential distribution and a characterization. Journal of Applied Probability
and Statistics, 9(1), 53-65.
[13] Athar, H., Nayabuddin and Zarrin, S. (2019). Generalized order statistics from
Marshall-Olkin extended exponential distribution. Journal of Statistical Theory and
Applications, 18(2), 129-135.
[14] Alharbi, Y. F., Athar, H. and Fawzy, M. A. (2021). Moment Properties of Generalized
Order Statistics from Exponentiated Generalized Class of Distributions. Thailand
Statistician, 19(4), 797-811.
[15] Athar, H., Noor, Z., Zarrin, S. and Almutairi, H. N. (2021). Expectation properties of
generalized order statistics from Poisson Lomax distribution. Statistics, Optimization
and Information Computing, 9(3), 735-747.
[16] Athar, H., Fawzy, M. A. and Alharbi, Y. F. (2023). Moment Properties of Generalized
Order Statistics Based on Modified Weighted Rayleigh Distribution. European
Journal of Statistics, 3, 1-1.
[17] Hwang, J. S. and Lin, G. D. (1984). Extensions of M¨untz-Sz´asz theorem and
applications. Analysis, 4(1-2), 143-160.
[18] Khan, A. H., Khan, R. U. and Yaqub, M. (2006). Characterization of continuous
distributions through conditional expectation of functions of generalized order
statistics. J. Appl. Probab. Statist, 1, 115-131.
[19] Huang, W. J. and Su, N. C. (2012). Characterizations of distributions based on
moments of residual life. Communications in Statistics-Theory and Methods, 41(15),
2750-2761.
[20] Ali, M. A. and Khan, A. H. (1998). Characterization of some types of distributions.
International journal of information and management sciences, 9, 1-10.
[21] Franco, M. and Ruiz, J. M. (1995). On characterization of continuous distributions
with adjacent order statistics. Statistics: A Journal of Theoretical and Applied
Statistics, 26(4), 375-385.
[22] Khan, A. H. and Abu-Salih, M. S. (1989). Characterizations of probability
distributions by conditional expectation of order statistics. Metron, 47, 171-181.
[23] Khan, A. H. and Abouammoh, A. M. (2000). Characterizations of distributions by
conditional expectation of order statistics. J. Appl. Statist. Sci, 9, 159-167.
[24] Balasubramanian, K. and Beg, M. I. (1992). Distributions determined by conditioning
on a pair of order statistics. Metrika, 39, 107-112.
[25] Athar, H. and Akhter, Z. (2015). Some characterization of continuous distributions
based on order statistics. International Journal of Computational and Theoretical
Statistics, 2(01) 31-36.
[26] Ahsanullah, M. (2017). Characterizations of univariate continuous distributions (Vol.
1). Amsterdam: Atlantis Press.
[27] e Noor, Z., Akhter, Z. and Athar, H. (2015). On characterization of probability
distributions through conditional expectation of generalized and dual generalized
order statistics. Pakistan Journal of Statistics, 31(2) 159-170.
[28] e Noor, Z., Athar, H. and Akhter, Z. (2014). Conditional expectation of generalized
order statistics and characterization of probability distributions. J. Stat. Appl. Pro.
Lett, 1(1), 9-18.
[29] Athar, H. and Abdel-Aty, Y. (2020). Characterization of general class of distributions
by truncated moment. Thailand Statistician, 18(2), 95-107.
[30] Ahsanullah, M., Ghitany, M. E. and Al-Mutairi, D. K. (2017). Characterization of
Lindley distribution by truncated moments. Communications in Statistics-Theory
and Methods, 46(12), 6222-6227.
[31] Glanzel, W. (1990). Some consequences of a characterization theorem based on
truncated moments. Statistics, 21(4), 613-618.
[32] Kotz, S. and Shanbhag, D. N. (1980). Some new approaches to probability
distributions. Advances in Applied Probability, 12(4), 903-921.
[33] Gradshteyn, I. S. and Ryzhik, I. M. (2014). Table of integrals, series, and products.
Academic press.
[34] Akhter, Z., MirMostafaee, S. M. T. K. and Ormoz, E. (2022). On the order statistics
of exponentiated moment exponential distribution and associated inference. Journal
of Statistical Computation and Simulation, 92(6), 1322-1346.
[35] Akhter, Z., Saran, J., Verma, K. and Pushkarna, N. (2020). Moments of order
statistics from length-biased exponential distribution and associated inference.
Annals of Data Science, 1-26.
[36] David, H. A. and Nagaraja, H. N. (2004). Order statistics. John Wiley and Sons.
Published
2025-01-09
How to Cite
Bakar, A., Athar, H., Alharbi, Y. F., & Fawzy, M. A. (2025). Moment Properties of Generalized Order Statistics From Lindley Pareto Distribution. Statistics, Optimization & Information Computing. https://doi.org/10.19139/soic-2310-5070-2026
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