Transmuted Mukherjee-Islam Distribution: A Generalization of Mukherjee-Islam Distribution

Alzoubi, Loai

doi:10.5539/jmr.v9n4p135

Cited by 3 publications

(1 citation statement)

References 10 publications

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“…Khan [19] obtained Reliability and Bayesian estimation of the parameter of Mukherjee-Islam distribution using assumptions of inverted gamma, uniform, and Siddiqui's priors, and the posterior distribution of each estimate were obtained in the literature. An extension of Mukherjee-Islam distribution was proposed by Al-Zou'bi [4] using quadratic transmutation map introduced by Shaw [27] and they studied Transmuted Mukherjee-Islam distribution. The density plot of this distribution has left skewed with an increasing failure rate.…”

Section: Introductionmentioning

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: Introductionmentioning

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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Gharaibeh Distribution and its Applications

2021

J. Stat. Appl. Prob.

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Epanechnikov-exponential distribution: properties and applications

Alkhazaalh

Alzoubi

2021

General Mathematics

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A new continuous distribution is proposed using Epanechnikov kernel function and the exponential distribution. This distribution is called the Epanechnikov-exponential distribution. Some properties of this distribution are studied. A simulation study is conducted to calculate the mean and the standard deviation of this distribution and to investigate the behavior of MLE to conserve the consistency property. An application to a real data set is conducted, it showed that he new distribution is more flexible than the exponential distribution.

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Transmuted Mukherjee-Islam Distribution: A Generalization of Mukherjee-Islam Distribution

Cited by 3 publications

References 10 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

Gharaibeh Distribution and its Applications

Epanechnikov-exponential distribution: properties and applications

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