Moments and inferences of inverted topp-leone distribution based on record values

M. J. S. Khan, Farhan Ansari, Qazi J. Azhad and Naresh Chandra Kabdwal ()
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M. J. S. Khan: Aligarh Muslim University
Farhan Ansari: Aligarh Muslim University
Qazi J. Azhad: Shiv Nadar University Institute of Eminence
Naresh Chandra Kabdwal: Banasthali Vidyapith

International Journal of System Assurance Engineering and Management, 2024, vol. 15, issue 6, No 48, 2623-2633

Abstract: Abstract In this article, the explicit expression for the moments of record values is derived from the inverted Topp-Leone distribution. We have also derived the recurrence relation for single and product moments of the inverted Topp-Leone distribution based on record values. These results were utilized to obtain the best linear unbiased estimator for the location and scale parameter of the inverted Topp-Leone distribution. The best linear unbiased predictor of future record is also computed. Further, based on records, the maximum likelihood estimator for the scale and shape parameters of the inverted Topp-Leone distribution is also derived. Also, the exact confidence intervals for scale and shape parameters of the inverted Topp-Leone distribution are constructed in terms of upper records. We have also conducted a simulation study to show the performances of derived point and interval estimators. In addition to that, we have also presented a real data study to discuss the significance of derived results in real-life scenarios. This study is useful when the data are heavily right-tailed, follow an inverted Topp-Leone distribution, and are in the form of a record sequence.

Keywords: Inverted topp-leone distribution; Records; Single moments; Product moments; Recurrence relations; Maximum likelihood estimator; Best linear unbiased estimator (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13198-024-02284-0

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