Best Linear Unbiased Estimator of the Parameter of the Rayleigh Distribution - Part I: Small Sample Theory for Censored Order Statistics

Dyer, Danny; Whisenand, Charles W.

doi:10.1109/tr.1973.5216019

Cited by 70 publications

(29 citation statements)

References 11 publications

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“…Hence, by applying this transformation to the data, all Rayleighity tests can be utilized for the purpose of testing the goodness-of-fit to the exponential distribution. Polovko (1969), and Dyer and Whisenand (1973), demonstrated the importance of this distribution in electro vacum devices and communication engineering. Also, the Rayleigh distribution was originally derived in connection with a problem in acoustics, and has been used as the distance distribution between individuals in a spatial Poisson process.…”

Section: Introductionmentioning

confidence: 99%

A Cumulative Residual Entropy Characterization of the Rayleigh Distribution and Related Goodness-of-Fit Test

Baratpour¹,

Khodadadi²

2013

JSRI

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Abstract. Rayleigh distribution is widely used for life-time modeling and is important in electro vacuum devices and communication engineering. Rao et al. (2004) suggested the Cumulative Residual Entropy (CRE), which is the extension of the Shannon entropy to the the cumulative distribution function. In this paper, a general class of maximum CRE distributions is introduced and then we characterize the Rayleigh distribution and use it to construct a goodness-of-fit test for ascertaining appropriateness of such model. For constructing the test statistics, we use Cumulative residual Kullback-Leibler information (CKL) that was introduced by Baratpour and Habibi (2012). Critical values for various sample sizes determined by means of Monte Carlo simulations are presented for the test statistics. A Monte Carlo power analysis is performed for various alternatives and sample sizes in order to compare the proposed test with several existing goodness-of-fit tests based on the empirical distribution. We find that the proposed test has good power properties. The use of the proposed test is shown in an illustrative example.

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Section: Introductionmentioning

confidence: 99%

A Cumulative Residual Entropy Characterization of the Rayleigh Distribution and Related Goodness-of-Fit Test

Baratpour¹,

Khodadadi²

2013

JSRI

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“…[Polovko (1968)] and [Dyer and Whisenand (1973)] demonstrated the importance of this distribution in electro vacuum devices and communication engineering.…”

Section: Rayleigh Lifetime Datamentioning

confidence: 99%

Estimating the parameters of lifetime distributions under progressively Type-II censoring from fuzzy data

Khoolenjani

Chatrabgoun

2016

Journal of Applied Mathematics, Statistics and Informatics

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The problem of estimating lifetime distribution parameters under progressively Type-II censoring originated in the context of reliability. But traditionally it is assumed that the available data from this censoring scheme are performed in exact numbers. However, some collected lifetime data might be imprecise and are represented in the form of fuzzy numbers. Thus, it is necessary to generalize classical statistical estimation methods for real numbers to fuzzy numbers. This paper deals with the estimation of lifetime distribution parameters under progressively Type-II censoring scheme when the lifetime observations are reported by means of fuzzy numbers. A new method is proposed to determine the maximum likelihood estimates of the parameters of interest. The methodology is illustrated with two popular models in lifetime analysis, the Rayleigh and Lognormal lifetime distributions.

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“…It was proposed by Lord Rayleigh for the first time in 1880. Since then several authors have discussed its properties and have developed inferential procedures under different situations in verity of fields; for details see, Dyer and Whisenand (1973), Bhattacharya and Tyagi (1990), Chung (1995), Dey and Maiti (2012).…”

Section: Introductionmentioning

confidence: 99%

Statistical Inferences of Type-II Progressively Hybrid Censored Fuzzy Data with Rayleigh Distribution

Chaturvedi

Singh

2018

AJS

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This article presents the procedures of parameter estimation based on Type-II progressively hybrid censored fuzzy lifetime data. Classical as well as the Bayesian procedures for the estimation of unknown model parameters has been developed. Keywords: Type-II progressive hybrid censoring, fuzzy lifetime data, Rayleigh distribution, maximum likelihood (ML) estimator, method of moments (MM) estimator, computational approach (CA) estimator.

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Best Linear Unbiased Estimator of the Parameter of the Rayleigh Distribution - Part I: Small Sample Theory for Censored Order Statistics

Cited by 70 publications

References 11 publications

A Cumulative Residual Entropy Characterization of the Rayleigh Distribution and Related Goodness-of-Fit Test

A Cumulative Residual Entropy Characterization of the Rayleigh Distribution and Related Goodness-of-Fit Test

Estimating the parameters of lifetime distributions under progressively Type-II censoring from fuzzy data

Statistical Inferences of Type-II Progressively Hybrid Censored Fuzzy Data with Rayleigh Distribution

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