Bayesian Estimation of the Parameter of Maxwell Distribution under Different Loss Functions

Dey, Sanku; Maiti, Sudhansu S.

doi:10.1080/15598608.2010.10411986

Cited by 18 publications

(11 citation statements)

References 4 publications

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“…Kamaljit and Kalpana [18] applied Bayesian and Semi-Bayesian approaches to estimate the parameters of the Generalized Inverse Weibull distribution. Other researches can be found in Dey and Maiti [10] , Rasheed [23] , AlBaldawi [5] , Adegoke et al [1] , Eraikhuemen et al [12] , Aijaz et al [2] and many more.…”

Section: Bayesian Estimation Of the Scale Parameter C Of Maxwell-mukherjee Islam Distributionmentioning

confidence: 99%

Bayesian estimation of the parameter of Maxwell-Mukherjee Islam distribution using assumptions of the Extended Jeffrey's, Inverse-Rayleigh and Inverse-Nakagami priors under the three loss functions

Ishaq

Abiodun

Falgore

2021

Heliyon

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A three-parameter Maxwell-Mukherjee Islam distribution was proposed by applying Maxwell generalized family of distributions introduced by Ishaq and Abiodun [17]. The probability density and cumulative distribution functions of the proposed distribution were defined. The validity test was derived from its cumulative distribution function. The study aimed to obtain a Bayesian estimation of the scale parameter of Maxwell-Mukherjee Islam distribution by using assumptions of the Extended Jeffrey's (Uniform, Jeffrey's and Hartigan's), Inverse-Rayleigh and Inverse-Nakagami priors under the loss functions, namely, Squared Error Loss Function (SELF), Precautionary Loss Function (PLF) and Quadratic Loss Function (QLF), and their performances were compared. The posterior distribution under each prior and its corresponding loss functions was derived. The performance of the Bayesian estimation was illustrated from the basis of quantile function by using a simulation study and application to real life data set. For different sample sizes and parameter values, the QLF and SELF under Jeffrey's and Hartigan's priors produced the same estimates, bias and Mean Squared Error (MSE) just as we observed in their mathematical derivatives. Similarly, the SELF, PLF and QLF under Inverse-Rayleigh and Inverse-Nakagami priors provided the same performance when some parameter values are equal. For some parameter values, the QLF under Inverse-Nakagami and Inverse-Rayleigh priors produced the least values of MSE. In the application to real life data set, the QLF and SELF under Jeffrey's and Hartigan's priors; the SELF, PLF and QLF under Inverse-Rayleigh and Inverse-Nakagami priors provided similar results as observed in the simulation study. Therefore, the study concluded that the QLF under Inverse-Rayleigh and Inverse-Nakagami priors could effectively be used in the estimation of scale parameter of Maxwell-Mukherjee Islam distribution using Bayesian approach.

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Section: Bayesian Estimation Of the Scale Parameter C Of Maxwell-mukherjee Islam Distributionmentioning

confidence: 99%

Bayesian estimation of the parameter of Maxwell-Mukherjee Islam distribution using assumptions of the Extended Jeffrey's, Inverse-Rayleigh and Inverse-Nakagami priors under the three loss functions

Ishaq

Abiodun

Falgore

2021

Heliyon

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“…In order to achieve the gap above, many researchers have used Bayesian estimation method for parameters of different probability distributions and a list of some of these studies is as follows: Bayesian estimation for the extreme value distribution using progressive censored data and asymmetric loss by [6], Bayesian estimators of the shape and scale parameters of modified Weibull distribution using Lindley's approximation under the squared error loss function, LINEX loss function and generalized entropy loss function by [7], comparison of Bayesian estimates of the shape parameter of Generalized Exponential Distribution based on a class of non-informative prior under the assumption of quadratic loss function, squared log-error loss function and general entropy loss function (GELF) and maximum likelihood estimates by [8], Bayesian Survival Estimator for Weibull distribution with censored data by [9] as well as [10], [11]. Similarly, [12] studied the shape parameter of generalized Rayleigh distribution under non-informative priors with a comparison to the method of maximum likelihood.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Estimation of the Scale Parameter of the Weimal Distribution

Mabur

Omale

Dewu³

et al. 2019

AJPAS

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This article aims at estimating the scale parameter of the Weimal distribution using Bayesian method and comparing the estimators obtained to the estimator of the scale parameter obtained from the method of maximum likelihood. Under Bayesian approach, the estimators are obtained by using uniform prior and Jeffrey’s prior with the adoption of the precautionary, quadratic and square error loss functions. A derivation and discussion2ws under maximum likelihood estimation is also done. The above methods of estimation employed in this paper are compared based on their mean square errors (MSEs) through a simulation study carried out in R statistical software with different sample sizes. The results indicate that the most appropriate method for the scale parameter is precautionary loss function under either uniform or Jeffrey’s prior irrespective of the sample sizes allocated and the values taken by the other parameters.

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“…Bekker and Roux [4] discussed the maximum likelihood estimator (MLE), Bayes estimators of the truncated first moment and hazard function of the Maxwell distribution. Dey and Maiti [5] derived Bayes estimators of Maxwell distribution by considering non-informative and conjugate prior distributions under three loss functions, namely, quadratic loss function, squared-log error loss function and MLINEX function. The references [6][7][8] studied the reliability estimation of Maxwell distribution based on Type-II censored sample, progressively Type-II censored sample and random censored sample, respectively.…”

Section: Introductionmentioning

confidence: 99%

“…This paper is devoted to the minimax estimation problem of the unknown scale parameterθ in the maxwell distribution with the following probability density function (pdf) (Dey and Maiti [5]):…”

Section: Introductionmentioning

confidence: 99%

Minimax Estimation of the Parameter of Maxwell Distribution Under Different Loss Functions

Li¹

2016

AJTAS

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The aim of this article is to study the Bayes estimation and minimax estimation of the parameter of Maxwell distribution. Bayes estimators are obtained with non-informative quasi-prior distribution under different loss functions, namely, weighted squared error loss, squared log error loss and entropy loss functions. Then the minimax estimators of the parameter are obtained by using Lehmann's theorem. Finally, performances of these estimators are compared in terms of risks.

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Bayesian Estimation of the Parameter of Maxwell Distribution under Different Loss Functions

Cited by 18 publications

References 4 publications

Bayesian estimation of the parameter of Maxwell-Mukherjee Islam distribution using assumptions of the Extended Jeffrey's, Inverse-Rayleigh and Inverse-Nakagami priors under the three loss functions

Bayesian estimation of the parameter of Maxwell-Mukherjee Islam distribution using assumptions of the Extended Jeffrey's, Inverse-Rayleigh and Inverse-Nakagami priors under the three loss functions

Bayesian Estimation of the Scale Parameter of the Weimal Distribution

Minimax Estimation of the Parameter of Maxwell Distribution Under Different Loss Functions

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