Bayes approach to study shape parameter of Frechet distribution

Nasir, Wajiha; Aslam, Muhammad

doi:10.14419/ijbas.v4i3.4644

Cited by 9 publications

(7 citation statements)

References 5 publications

(2 reference statements)

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“…(Abbas et al, 2012) suggested numerical methods for the derivation of the posterior distribution and Bayes estimators under informative and non-informative priors. (Nasir & Aslam, 2015) used the quadrature numerical integration technique for solving the posterior distribution. The Bayes estimators and associated posterior risk of the parameters of L-G{F} distribution are derived by taking the expectation of a function of parameters under posterior distributions defined in equations( 8), (10), and (12).…”

Section: Bayes Point Estimationmentioning

confidence: 99%

Exploring Lomax-Gumbel {Frechet} Distribution in the Bayesian Paradigm

Ateeq¹,

Safdar²

2022

JSCIR

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This paper explores the Lomax-Gumbel {Frechet} distribution in the Bayesian paradigm. The posterior distributions of the parameters are not attained in closed form, so the Lindley and the Tierney-Kadane approximation methods are used for the evaluation of Bayes estimators and associated posterior risks under uniform, Maxwell, and half logistic priors. A complete implementation of these two techniques is provided. Three loss functions are used. An extensive simulation study and two real life data are provided to obtain and compare Bayes estimators in terms of prior distributions and loss functions. It is reported that the Bayes estimators obtained through the Tierney-Kadane method give better results than the Lindley approximation method, in terms of minimum posterior risks.

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Section: Bayes Point Estimationmentioning

confidence: 99%

Exploring Lomax-Gumbel {Frechet} Distribution in the Bayesian Paradigm

Ateeq¹,

Safdar²

2022

JSCIR

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“…Furthermore, Abbas and Yincai [12] conducted a comparative analysis of the scale parameter estimation for the Fréchet distribution, employing maximum likelihood, probability-weighted moments, and Bayes estimations. Nasir and Aslam [13] utilized a Bayesian technique to estimate the parameter of the Fréchet distribution. Reyad et al [14] established QE-Bayes and E-Bayes estimates for the scale parameters associated with the Fréchet distribution.…”

Section: Introductionmentioning

confidence: 99%

Properties and Maximum Likelihood Estimation of the Novel Mixture of Fréchet Distribution

Phaphan,

Abdullahi,

Puttamat

2023

Symmetry

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In recent decades, there have been numerous endeavors to develop a novel category of survival distributions possessing enhanced flexibility through the extension of existing distributions. This article constructs and validates the statistical properties of a novel survival distribution in order to obtain an alternative distribution that is suitable for analyzing survival data by presenting the novel mixture of the Fréchet distribution along with statistical properties such as the probability density function (PDF), cumulative distribution function (CDF), rth ordinary moment, skewness, kurtosis, moment-generating function, mean, variance, mode, survival function, hazard function, and asymptotic behavior, as well as constructing the estimators of the unknown parameter by employing the expectation-maximization (EM) algorithm, and simulated annealing. Additionally, the performance of the proposed estimators was compared with bias, mean squared errors (MSE), and simulated variances, and given an illustrative example of the proposed distribution to the survival data set in order to show that the proposed distribution is appropriate for the right-skewed data. This will be extremely advantageous in survival analysis.

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“…[6] derived the reference and matching priors for the Frechet stress-strength model and developed Bayesian approach for Frechet distribution under reference prior, respectively. [7] attained Bayesian estimators of Frechet distribution and their risks by using loss functions under Gumbel Type-II prior and Levy prior. Likewise, [8] estimated the Frechet distribution parameters with an application to the medical field.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Study Using MCMC of Three-Parameter Frechet Distribution Based on Type-I Censored Data

Ahmed¹

2021

JAMP

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Type-I censoring mechanism arises when the number of units experiencing the event is random but the total duration of the study is fixed. There are a number of mathematical approaches developed to handle this type of data. The purpose of the research was to estimate the three parameters of the Frechet distribution via the frequentist Maximum Likelihood and the Bayesian Estimators. In this paper, the maximum likelihood method (MLE) is not available of the three parameters in the closed forms; therefore, it was solved by the numerical methods. Similarly, the Bayesian estimators are implemented using Jeffreys and gamma priors with two loss functions, which are: squared error loss function and Linear Exponential Loss Function (LINEX). The parameters of the Frechet distribution via Bayesian cannot be obtained analytically and therefore Markov Chain Monte Carlo is used, where the full conditional distribution for the three parameters is obtained via Metropolis-Hastings algorithm. Comparisons of the estimators are obtained using Mean Square Errors (MSE) to determine the best estimator of the three parameters of the Frechet distribution. The results show that the Bayesian estimation under Linear Exponential Loss Function based on Type-I censored data is a better estimator for all the parameter estimates when the value of the loss parameter is positive.

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Bayes approach to study shape parameter of Frechet distribution

Cited by 9 publications

References 5 publications

Exploring Lomax-Gumbel {Frechet} Distribution in the Bayesian Paradigm

Exploring Lomax-Gumbel {Frechet} Distribution in the Bayesian Paradigm

Properties and Maximum Likelihood Estimation of the Novel Mixture of Fréchet Distribution

Bayesian Study Using MCMC of Three-Parameter Frechet Distribution Based on Type-I Censored Data

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