Exploring an extension of the Rayleigh distribution‎: ‎statistical estimation and practical application

Document Type : Original Article

Authors

Harsh Tripathi ¹

Varun Agiwal ²

¹ Symbiosis Statistical Institute, Symbiosis International (Deemed University), Pune, India

² Indian Institute of Public Health, Hyderabaad, India

10.22067/smps.2026.93521.1047

Abstract

‎In this paper‎, ‎we introduce a new extension of the Rayleigh distribution‎, ‎termed the Rayleigh-Exponential distribution (Ra-Ex-D)‎. ‎The proposed distribution is capable of modeling a wide range of data behaviors and demonstrates greater flexibility compared to classical distributions‎. ‎Several statistical properties of the proposed distribution are derived‎, ‎including survival characteristics‎, ‎mean deviation‎, ‎entropy‎, ‎and conditional moments‎, ‎along with the necessary proofs‎. ‎Model parameters are estimated using both classical and Bayesian approaches under different prior assumptions‎. ‎A simulation study is conducted to assess the performance of the estimation methods‎, ‎demonstrating that the proposed procedures yield reliable and consistent estimates‎. ‎Furthermore‎, ‎the practical applicability of the model is illustrated through the analysis of a real-life dataset‎, ‎where the proposed distribution exhibits superior fitting performance compared to existing models‎.

Keywords

Bayesian estimation

Classical estimation

Moments

Rayleigh distribution

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