Moments and estimation of Burr Hatke Exponential model based on generalized order statistics with real data applications

Farhan Ansari; M. J. S.  Khan

doi:https://doi.org/10.59139/stattrans-2026-034

Moments and estimation of Burr Hatke Exponential model based on generalized order statistics with real data applications

Farhan Ansari Department of Statistics and Operations Research, Aligarh Muslim University, Aligarh, India ORCID:https://orcid.org/0000-0002-8199-0047 , M. J. S. Khan Department of Statistics and Operations Research, Aligarh Muslim University, Aligarh, India ORCID:https://orcid.org/0000-0003-2264-9815 Statistics in Transition new series, vol. 27, 2026, 3, pages: 207-228 Published online: 9 September 2026 https://doi.org/10.59139/stattrans-2026-034 Citation: Ansari F., Khan M. J. S., 2026. Moments and estimation of Burr-Hatke Exponential model based on generalized order statistics with real data applications. Statistics in Transition new series, 27(3), pp. 207-228. https://doi.org/10.59139/stattrans-2026-034

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ABSTRACT

This paper presents a recurrence relation for single and product moments of the Burr-Hatke exponential distribution based on generalized order statistics and record values. Moreover, we have derived the explicit and exact expressions for the single moment of generalized order statistics from the Burr-Hatke exponential distribution. Furthermore, the classical and Bayesian estimation procedures for estimating the Burr-Hatke exponential distribution parameter are discussed when the data are in the form of records and gos. In addition, the asymptotic confidence interval, boot-p confidence interval, and credible interval for the parameter of the Burr-Hatke exponential distribution are discussed. Monte Carlo simulations were conducted to evaluate the performance of the estimators derived from both classical and Bayesian approaches, with a particular emphasis on their mean squared error. Moreover, two real datasets are included for illustrative purposes in this study.

KEYWORDS

Generalized order statistics, single moments, recurrence relations, Burr Hatke exponential distribution, MLE, Bayesian estimation, credible interval.

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