Exponentiated Mukherjee-Islam Distribution

Rather, Aafaq A.; Subramanian, Chelakara

doi:10.18576/jsap/070213

Cited by 11 publications

(7 citation statements)

References 1 publication

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“…Many authors focused on the exponentiated distributions and its applications; for example, Nadarajah and Kotz [1], Ali et al [2], Silva et al [3], Lemonte et al [4], Elgarhy and Shawki [5] and Rather and Subramanian [6].…”

Section: Introductionmentioning

confidence: 99%

Bayesian Estimation and Prediction for Exponentiated Generalized Inverted Kumaraswamy Distribution Based on Dual Generalized Order Statistics

AL-Fattah

El-Kader

EL-Helbawy

et al. 2021

JAMCS

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In this paper, the shape parameters, reliability and hazard rate functions of the exponentiated generalized inverted Kumaraswamy distribution are estimated using Bayesian approach. The Bayes estimators are derived under the squared error loss function and the linear-exponential loss function based on dual generalized order statistics. Credible intervals for the parameters, reliability and hazard rate functions are obtained. The Bayesian prediction (point and interval) for a future observation of the exponentiated generalized inverted Kumaraswamy distribution is obtained based on dual generalized order statistics. All results are specialized to lower record values and a numerical study is presented. Moreover, the theoretical results are applied on three real data sets.

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Section: Introductionmentioning

confidence: 99%

Bayesian Estimation and Prediction for Exponentiated Generalized Inverted Kumaraswamy Distribution Based on Dual Generalized Order Statistics

AL-Fattah

El-Kader

EL-Helbawy

et al. 2021

JAMCS

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“…Many researchers have considered the Mukherjee-Islam model as a lifetime distribution and applied it in various areas of statistical applications including Siddiqui [29] who studied the physical properties parameters were derived. A three-parameter lifetime distribution was introduced by Rather [24] by adding an extra shape parameter to study Exponentiated Mukherjee-Islam distribution. Several properties of this distribution including moments, harmonic mean, moment generating function, Renyi, and Shanon entropies were discussed.…”

Section: Introductionmentioning

confidence: 99%

“…The order statistics, moments, entropies, moment generating function, and estimates of the parameters were derived. A three-parameter lifetime distribution was introduced by Rather [24] by adding an extra shape parameter to study Exponentiated Mukherjee-Islam distribution. Several properties of this distribution including moments, harmonic mean, moment generating function, Renyi, and Shanon entropies were discussed.…”

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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“…Pal et al (2006) studied the exponentiated Weibull family as an extension of Weibull distribution. Rather and Subramanian [9] discussed the exponentiated Mukharjee-Islam distribution which shows more flexibility than the classical distribution. The same authors [10] published an exponentiated Garima distribution and discussed its application with engineering science data.…”

Section: Introductionmentioning

confidence: 99%

Exponentiated Frechet Distribution with Application in Temperature of Assam, India Overview with New Properties and Estimation

Rahman

Roy

2021

AJPAS

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In this paper, a new kind of distribution has suggested with the concept of exponentiate. The reliability analysis including survival function, hazard rate function, reverse hazard rate function and mills ratio has been studied here. Its quantile function and order statistics are also included. Parameters of the distribution are estimated by the method of Maximum Likelihood estimation method along with Fisher information matrix and confidence intervals have also been given. The application has been discussed with the 30 years temperature data of Silchar city, Assam, India. The goodness of fit of the proposed distribution has been compared with Frechet distribution and as a result, for all 12 months, the proposed distribution fits better than the Frechet distribution.

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Exponentiated Mukherjee-Islam Distribution

Cited by 11 publications

References 1 publication

Bayesian Estimation and Prediction for Exponentiated Generalized Inverted Kumaraswamy Distribution Based on Dual Generalized Order Statistics

Bayesian Estimation and Prediction for Exponentiated Generalized Inverted Kumaraswamy Distribution Based on Dual Generalized Order Statistics

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

Exponentiated Frechet Distribution with Application in Temperature of Assam, India Overview with New Properties and Estimation

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