Bayesian Estimation of the Transmuted Fréchet Distribution

Yousaf, Rahila; Aslam, Muhammad; Ali, Sajid

doi:10.1007/s40995-018-0581-1

Cited by 8 publications

(3 citation statements)

References 23 publications

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“…different posterior summaries. Thus, we adopt a Markov Chain Monte Carlo (MCMC) technique as have been used by Ali (2015) and Yousaf et al (2018).…”

Section: Posterior Summaries By Markov Chain Monte Carlo (Mcmc)mentioning

confidence: 99%

Bayesian Estimation of Transmuted Weibull Distribution under Different Loss Functions

Yousaf

Ali

Aslam

2020

JRSS

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In this article, we aim to estimate the parameters of the transmuted Weibull distribution (TWD) using Bayesian approach, as the Weibull distribution plays an important role in reliability engineering and life testing problems. Informative and non-informative priors under squared error loss function (SELF), precautionary loss function (PLF) and quadratic loss function (QLF) are assumed to estimate the scale, the shape and the transmuted parameter of the TWD. In addition to this, we also compute the Bayesian credible intervals (BCIs). To estimate parameters, we adopt Markov Chain Monte Carlo (MCMC) technique assuming uncensored and censored environments in terms of different sample sizes and censoring rates. The posterior risks, associated with each estimator are used to compare the performance of different estimators. Two real data sets are analyzed to illustrate the flexibility of the proposed distribution.

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“…different posterior summaries. Thus, we adopt a Markov Chain Monte Carlo (MCMC) technique as have been used by Ali (2015) and Yousaf et al (2018).…”

Section: Posterior Summaries By Markov Chain Monte Carlo (Mcmc)mentioning

confidence: 99%

Bayesian Estimation of Transmuted Weibull Distribution under Different Loss Functions

Yousaf

Ali

Aslam

2020

JRSS

Self Cite

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“…In this case, the Bayesian approach is advantageous due to the incorporation of prior knowledge about these parameters through prior distributions (Migon et al, 2014). Furthermore, although most studies assume a normal distribution for data, the Bayesian approach allows applying other distributions, such as the asymmetric one (Yousaf et al, 2019;Aslam et al, 2020), and the analysis of categorical data (Montesinos López et al, 2022). Since the impact of prior distribution in inferences increases as the sample size decreases (Tang, 2020), the elicitation of the prior distribution must be carried out with caution, and more informative prior distributions should be used instead of non-informative prior distributions (Van de Schoot et al, 2015.…”

Section: Introductionmentioning

confidence: 99%

Informative prior distribution applied to linseed for the estimation of genetic parameters using a small sample size

Azevedo

Carvalho

Nascimento

et al. 2022

Pesq. agropec. bras.

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The objective of this work was to evaluate a procedure for the elicitation of informative prior distribution, compared with non-informative prior distribution, in a small sample size, using 14 traits of three linseed (Linum usitatissimum) genotypes in seven sowing seasons. The values of the hyperparameters regulate the informativeness of the prior distribution; therefore, for each season, the hyperparameters to be used in the next season were calculated. The two prior distributions, non-informative and informative, were compared by the length of the credible interval and variance of the posterior distribution. In general, when the informative prior distribution is adopted, the genetic parameters present a shorter length of the credible interval and more precise estimates. The mechanism for informative prior elicitation using previous information from breeding programs is efficient for the estimation of genetic parameters, including heritability and genetic variance, even when the sample size is small. In genetic evaluation, the use of informative prior distribution is better than that of non-informative distribution for a small sample size. In general, the results of the informative prior distributions are indicative that the genetic values of the first sowing season are greater for the following traits: cycle length, plant height, and number of non-grained capsules and of productive branches.

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“…Hemantha introduced an MCMC simulation method to engineering economics research [15]. Yousaf [16] considered transmuted distribution and compared priors under the squared error loss function. Begona, et al [17] developed a new technique to estimate the SIR model parameters using the MCMC method.…”

Section: Introductionmentioning

confidence: 99%