Bayesian Analysis of Power Function Distribution under Double Priors

Sultan, Raja; Sultan, Hummara; Ahmad, Sajjad

doi:10.12785/jsap/030214

Cited by 8 publications

(6 citation statements)

References 4 publications

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“…Omar and Low [ 9 ] developed the Bayesian estimate for the shape parameter of the generalized power function distribution by considering both the informative and non-informative priors under mean square error loss function. Moreover, Sultan et al [ 10 ] estimated the scale parameter of the power function distribution by using Bayesian method with three double types of priors and three single types of priors’ distributions. Bhatt [ 11 ] showed the characterization of power function distribution through expectation of non-constant function of a random variable.…”

Section: Introductionmentioning

confidence: 99%

Comparison of Two New Robust Parameter Estimation Methods for the Power Function Distribution

Shakeel¹,

Haq

Hussain

et al. 2016

PLoS ONE

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Estimation of any probability distribution parameters is vital because imprecise and biased estimates can be misleading. In this study, we investigate a flexible power function distribution and introduced new two methods such as, probability weighted moments, and generalized probability weighted methods for its parameters. We compare their results with L-moments, trimmed L-moments by a simulation study and a real data example based on performance measures such as, mean square error and total deviation. We concluded that all the methods perform well in the case of large sample size (n>30), however, the generalized probability weighted moment method performs better for small sample size.

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Section: Introductionmentioning

confidence: 99%

Comparison of Two New Robust Parameter Estimation Methods for the Power Function Distribution

Shakeel¹,

Haq

Hussain

et al. 2016

PLoS ONE

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“…To derive the posterior distributions for the parameter θ, using a combination of two prior distributions such gamma distribution [8] with Erlang distribution [7] and Erlang distribution with exponential distribution [1],and Erlang distribution with non-informative distribution and exponential distribution with non-informative distribution.…”

Section: Bayes Estimation Methodsmentioning

confidence: 99%

The Bayesian Estimation for The Shape Parameter of The Power Function Distribution (PFD-I) to Use Hyper Prior Functions

Al-obedy¹

2021

JEAS

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The objective of this study is to examine the properties of Bayes estimators of the shape parameter of the Power Function Distribution (PFD-I), by using two different prior distributions for the parameter θ and different loss functions that were compared with the maximum likelihood estimators. In many practical applications, we may have two different prior information about the prior distribution for the shape parameter of the Power Function Distribution, which influences the parameter estimation. So, we used two different kinds of conjugate priors of shape parameter θ of the Power Function Distribution (PFD-I) to estimate it. The conjugate prior function of the shape parameter θ was considered as a combination of two different prior distributions such as gamma distribution with Erlang distribution and Erlang distribution with exponential distribution and Erlang distribution with non-informative distribution and exponential distribution with the non-informative distribution. We derived Bayes estimators for shape parameter θ of the Power Function Distribution (PFD-I) according to different loss functions such as the squared error loss function (SELF), the weighted error loss function (WSELF) and modified linear exponential (MLINEX) loss function (MLF), with two different double priors. In addition to the classical estimation (maximum likelihood estimation). We used simulation to get the results of this study, for different cases of the shape parameter of the Power Function Distribution used to generate data for different samples sizes.

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“…Skaeel et al [ 13 ] estimated the parameters of PF using L-moments, TL-moments, probability weighted moments (PWM) and generalized PWM. Bayesian analysis of PF distribution is discussed using single and double priors by [ 14 ].…”

Section: Introductionmentioning

confidence: 99%

A new cubic transmuted power-function distribution: Properties, inference, and applications

et al. 2023

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A new three-parameter cubic transmuted power distribution is proposed using the cubic rank transformation. The density and hazard functions of the new distribution provide great flexibility. Some mathematical properties of the new model such as quantile function, moments, dispersion index, mean residual life, and order statistics are derived. The model parameters are estimated using five different estimation methods. A comprehensive simulation study is carried out to understand the behavior of derived estimators and choose the best estimation method. The usefulness of the proposed distribution is illustrated using a real dataset. It is concluded that the proposed distribution is better than some well-known existing distributions.

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Bayesian Analysis of Power Function Distribution under Double Priors

Cited by 8 publications

References 4 publications

Comparison of Two New Robust Parameter Estimation Methods for the Power Function Distribution

Comparison of Two New Robust Parameter Estimation Methods for the Power Function Distribution

The Bayesian Estimation for The Shape Parameter of The Power Function Distribution (PFD-I) to Use Hyper Prior Functions

A new cubic transmuted power-function distribution: Properties, inference, and applications

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