Moments and Inferences based on Generalized Order Statistics from Benktander Type II Distribution
Keywords:
Generalized order statistics (gos), record values, order statistics, single moments, recurrence relations, Benktander Type II distribution, characterization and Maximum likelihood estimator
Abstract
In this paper, we employ generalized order statistics to investigate the moment properties of the Benktander Type II distribution. Through this approach, we derive precise and explicit formulas for single moments and establish recurrence relations for single and product moments. Additionally, we present a characterization of the Benktander Type II distribution, accompanied by further implications regarding moments of record values and ordinary order statistics. We estimate the unknown parameters of the Benktander Type II distribution using Maximum Likelihood (ML) estimation for generalized order statistics (gos). Subsequently, we conduct simulation studies encompassing order statistics. The efficacy of the obtained ML estimates is evaluated through comprehensive simulation analyses, focusing on various moments and their relative mean squared errors. This research contributes to understanding the Benktander Type II distribution's properties and provides valuable insights into its parameter estimation using generalized order statistics.References
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and Statistics, vol. 7, pp. 106–113, 2018.
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[3] M. Ahsanullah, “Generalized order statistics from exponential distribution,” Journal of Statistical planning and Inference, vol. 85, no. 1-2, pp. 85–91, 2000.
[4] E. K. Al-Hussaini, A. E.-B. A. Ahmad, and M. Al-Kashif, “Recurrence relations
for moment and conditional moment generating functions of generalized order
statistics,” Metrika, vol. 61, no. 2, pp. 199–220, 2005.
[5] M. Faizan and H. Athar, “Moments of generalized order statistics from a general
class of distributions,” Journal of Statistics, vol. 15, pp. 36–43, 2008.
[6] D. Kumar, “Moment generating functions of generalized order statistics from extended type ii generalized logistic distribution.,” J. Stat. Theory Appl., vol. 13,
no. 4, pp. 273–288, 2014.
[7] R. Khan and M. Khan, “Moment properties of generalized order statistics from
exponential-weibull lifetime distribution,” Journal of advanced statistics, vol. 1,
no. 3, p. 147, 2016.
[8] D. Kumar and S. Dey, “Relations for moments of generalized order statistics
from extended exponential distribution,” American Journal of Mathematical and
Management Sciences, vol. 36, no. 4, pp. 378–400, 2017.
[9] N. Gupta, Z. Anwar, and A. A. Dar, “Moment properties of generalized order
statistics from ailamujia distribution,” International Journal of Computational
and Theoretical Statistics, vol. 5, no. 02, pp. 115–122, 2018.
[10] N. Gupta and Q. A. Jamal, “Inference for weibull generalized exponential distribution based on generalized order statistics,” Journal of Applied Mathematics and
Computing, vol. 61, no. 1, pp. 573–592, 2019.
[11] N. Gupta and Z. Anwar, “Relations for single and product moments of odds generalized exponential-pareto distribution based on generalized order statistics and
its characterization,” Statistics, Optimization & Information Computing, vol. 7,
no. 1, pp. 160–170, 2019.
[12] M. R. Malik and D. Kumar, “Generalized pareto distribution based on generalized
order statistics and associated inference,” Statistics in Transition New Series,
vol. 20, no. 3, 2019.
[13] M. Khan, A. Sharma, and S. Iqrar, “On moments of lindley distribution based on
generalized order statistics,” American Journal of Mathematical and Management
Sciences, vol. 39, no. 3, pp. 214–233, 2020.
21
[14] D. Kumar, M. Nassar, and S. Dey, “Inference for generalized inverse lindley distribution based on generalized order statistics,” Afrika Matematika, vol. 31, no. 7-8,
pp. 1207–1235, 2020.
[15] D. Kumar, “Lower generalized order statistics based on inverse burr distribution,” American Journal of Mathematical and Management Sciences, vol. 35, no. 1,
pp. 15–35, 2016.
[16] M. Alam, R. Khan, and Z. Vidovic, “Moments of generalized order statistics for
pareto-rayleigh distribution,”
[17] M. Anas, A. A. Dar, A. Ahmed, and M. Arshad, “K th-order equilibrium weibull
distribution: properties, simulation, and its applications,” Communications in
Statistics-Simulation and Computation, pp. 1–23, 2023.
[18] Z. Anwar, A. N. Khan, and N. Gupta, “Expectation identities of generalized order
statistics from the bass diffusion model,” Thailand Statistician, vol. 20, no. 1,
pp. 16–25, 2022.
[19] C. Kleiber and S. Kotz, Statistical size distributions in economics and actuarial
sciences. John Wiley & Sons, 2003.
[20] G. Benktander and C.-O. Segerdahl, “On the analytical representation of claim
distributions with special reference to excess of loss reinsurance,” in Transactions
of the h˜ ternational Congress of Actuaries, 1960.
[21] G. Benktander, “Schadenverteilung nach gr¨osse in der nicht-leben-versicherung,”
Bulletin of the Swiss Association of Actuaries, pp. 263–283, 1970.
[22] N. Kilany and W. Hassanein, “Characterization of benktander type ii distribution
via truncated moments and order statistics,” International Journal of Probability
and Statistics, vol. 7, pp. 106–113, 2018.
[23] J. Hwang and G. Lin, “On a generalized moment problem. ii,” Proceedings of the
American Mathematical Society, vol. 91, no. 4, pp. 577–580, 1984
Published
2025-01-29
How to Cite
Anwar, Z., Ali, Z., Faizan, M., & Khan, I. (2025). Moments and Inferences based on Generalized Order Statistics from Benktander Type II Distribution. Statistics, Optimization & Information Computing. Retrieved from http://47.88.85.238/index.php/soic/article/view/2001
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Section
Research Articles
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