Abstract
This paper discusses the sequential estimation of the scale parameter of the Rayleigh distribution using the three-stage sequential sampling procedure proposed by Hall (Ann. Stat.1981, 9, 1229–1238). Both point and confidence interval estimation are considered via a unified optimal decision framework, which enables one to make the maximum use of the available data and, at the same time, reduces the number of sampling operations by using bulk samples. The asymptotic characteristics of the proposed sampling procedure are fully discussed for both point and confidence interval estimation. Since the results are asymptotic, Monte Carlo simulation studies are conducted to provide the feel of small, moderate, and large sample size performance in typical situations using the Microsoft Developer Studio software. The procedure enjoys several interesting asymptotic characteristics illustrated by the asymptotic results and supported by simulation.
Highlights
Let X1,X2, X3, . . . be independent and identically distributed random variables following a Rayleigh distribution with unknown scale parameter σ of the form: f (x; σ) = x −x2 /2σ2, x > 0 and σ > 0. e σ2The survival or reliability function is e−x /2σ and the hazard function is x/σ2 for all x > 0 and σ > 0
This paper aims to estimate sequentially the scale parameter σ of the Rayleigh distribution using a multistage sampling procedure, the three-stage procedure, that was presented by Hall [24]
Since the stopping variable N depends on the scale parameter estimate TN, N and TN are not stochastically independent
Summary
Let X1 ,X2 , X3 , . . . be independent and identically distributed random variables following a Rayleigh distribution with unknown scale parameter σ of the form:. Be independent and identically distributed random variables following a Rayleigh distribution with unknown scale parameter σ of the form:. The reliability function decreases at a much higher rate than the exponential distribution’s reliability function, whose hazard rate is constant (see Kodlin [1]) This distribution relates to several distributions, such as generalized extreme value, Weibull, and Chi-square, and its applicability in real-life situations is significant. Symmetry 2020, 12, 1925 propagation through a scattering medium Others, such as Siddiqui [7], Hirano [8], and Howlader and Hossian [9], discussed several aspects of the Rayleigh distribution. This paper aims to estimate sequentially the scale parameter σ of the Rayleigh distribution using a multistage sampling procedure, the three-stage procedure, that was presented by Hall [24].
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