Shrinkage Estimation in the Inverse Rayleigh Distribution

Prakash, Gyan

doi:10.22237/jmasm/1272687540

Cited by 4 publications

(6 citation statements)

References 17 publications

(11 reference statements)

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“…The results of the simulation study for estimating the scale parameter (θ) were summarized and tabulated in tables (1), (2) and (3) which are contain the expected values and MSE's for different estimates of the scale parameter, while tables (4), (5) and (6) are contain IMSE's for different estimate of the Reliability function. We have observed that: 1.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…Also, In (2013) Prakash discuss the Bayes estimation in the inverse Rayleigh model under two different loss functions (Square error, LINEX loss function) [5]. In (2014) Khan obtained, the Modified inverse Rayleigh distribution is special case of inverse Weibll, which is extension to it [6]. In (2015) the Fan discuss Bayes Estimation for Inverse Rayleigh model under different loss functions squared error loss, LINEX loss and entropy loss functions [7].…”

Section: Introductionmentioning

confidence: 99%

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Comparison of Bayes Estimators for Parameter and Relia-bility Function for Inverse Rayleigh Distribution by Using Generalized Square Error Loss Function

Rasheed¹

2018

MJS

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In the current study, we have been derived some Basyian estimators for the parameter and relia-bility function of the inverse Rayleigh distribution under Generalized squared error loss function. In order to get the best understanding of the behavior of Bayesian analysis, we consider non-informative prior for the scale parameter using Jefferys prior Information as well as informative prior density represented by Gamma distribution. Monte-Carlo simulation have been employed to compare the behavior of different estimates for the scale parameter and reliability function of in-verse Rayleigh distribution based on mean squared errors and Integrated mean squared errors, respectively. In the current study, we observed that more occurrence of Bayesian estimate using Generalized squared error loss function using Gamma prior is better than other estimates for all cases

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Section: Simulation Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Comparison of Bayes Estimators for Parameter and Relia-bility Function for Inverse Rayleigh Distribution by Using Generalized Square Error Loss Function

Rasheed¹

2018

MJS

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“…Kim and Han (2009) considered estimation of the scale parameter of the Rayleigh distribution under general progressive censoring. Mousa et al (2005;Prakash, 2013) focused on Bayesian prediction and Bayesian estimation for Rayleigh models.…”

Section: Jmssmentioning

confidence: 99%

Sequential Estimation of the Square of the Rayleigh Parameter

Tahir¹

2014

Journal of Mathematics and Statistics

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“…Inverse Rayleigh distribution (IRD) has raised growing interest in modeling positive random variables and especially for its applications in reliability and survival times studies [1][2][3][4][5][6][7][8][9][10][11]. Being also a particular case of the inverse Weibull distribution, which has been adopted as a valid model for the characterization and estimation of extreme values of wind speed (WS) [12][13][14][15][16][17]-or briefly, "extreme wind speed" (EWS)-the IRD model is studied in this paper in relation to such kinds of applications.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Extreme Wind Speed Modeling and Bayes Estimation under the Inverse Rayleigh Distribution

Chiodo

Noia

2020

Applied Sciences

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Inverse Rayleigh probability distribution is shown in this paper to constitute a valid model for characterization and estimation of extreme values of wind speed, thus constituting a useful tool of wind power production evaluation and mechanical safety of installations. The first part of this paper illustrates such a model and its validity to interpret real wind speed field data. The inverse Rayleigh model is then adopted as the parent distribution for assessment of a dynamical “risk index” defined in terms of a stochastic Poisson process, based upon crossing a given value with part of the maximum value of wind speed on a certain time horizon. Then, a novel Bayes approach for the estimation of such an index under the above model is proposed. The method is based upon assessment of prior information in a novel way which should be easily feasible for a system engineer, being based upon a model quantile (e.g., the median value) or, alternatively, on the probability that the wind speed is greater than a given value. The results of a large set of numerical simulation—based upon typical values of wind-speed parameters—are reported to illustrate the efficiency and the precision of the proposed method, also with hints to its robustness. The validity of the approach is also verified with respect to the two different methods of assessing the prior information.

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Shrinkage Estimation in the Inverse Rayleigh Distribution

Abstract: The properties of the shrinkage test-estimators of the parameter were studied for an inverse Rayleigh model under the asymmetric loss function. Both the single and double-stage shrinkage test-estimators are considered.

Cited by 4 publications

References 17 publications

Comparison of Bayes Estimators for Parameter and Relia-bility Function for Inverse Rayleigh Distribution by Using Generalized Square Error Loss Function

Comparison of Bayes Estimators for Parameter and Relia-bility Function for Inverse Rayleigh Distribution by Using Generalized Square Error Loss Function

Sequential Estimation of the Square of the Rayleigh Parameter

Stochastic Extreme Wind Speed Modeling and Bayes Estimation under the Inverse Rayleigh Distribution

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