Comparing Classical and Sequential Parameter Estimation in Power Rayleigh Distribution
DOI:
https://doi.org/10.13052/jrss0974-8024.1927Keywords:
Sequential probability ratio test, operating characteristics, average sample number, acceptance and rejection regions, power Rayleigh distribution, Neyman-Pearson procedure, Type I error and Type II errorAbstract
This study explores the novel application of the performance characteristics of sequential probability ratio test (SPRT) for estimation the scale parameter (θ) of the power Rayleigh distribution, focusing on its scale parameters (θ) that are the fundamental to defining its properties and shaping the statistical characteristics. For testing the null hypothesis H0:θ=θ0 versus H1:θ=θ1, a stop rule method is utilized to optimize the sample size. Through this approach, we derive approximations for key performances metrics, including the operating characteristic (OC) function and the average sample number (ASN). The study also confirms the existence of the function L(θ), necessary to meet the ASN requirements in sequential testing. The new method is comprised of the efficiency of the SPRT compared to the classical Neyman-Pearson (N-P) technique. A comprehensive simulation study shows that the proposed method of SPRT significantly reduces the sample size required for the hypothesis testing by 65.99% to 77.49% compared to the Neyman-Pearson (N-P) test without compromising accuracy.
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