Bayes inference under a finite mixture of two-compound Gompertz components model

Recently, Rayleigh distribution has received considerable attention in the statistical literature. In this paper, we consider the point and interval estimation of the functions of the unknown parameters of a two-parameter Rayleigh distribution. First, we obtain the maximum likelihood estimators (MLEs) of the unknown parameters. The MLEs cannot be obtained in explicit forms, and we propose to use the maximization of the profile log-likelihood function to compute the MLEs. We further consider the Bayesian inference of the unknown parameters.The Bayes estimates and the associated credible intervals cannot be obtained in closed forms.We use the importance sampling technique to approximate (compute) the Bayes estimates and the associated credible intervals. For comparison purposes we have also used the exact method to compute the Bayes estimates and the corresponding credible intervals. Monte Carlo simulations are performed to compare the performances of the proposed method, and one data set has been analyzed for illustrative purposes. We further consider the Bayes prediction problem based on the observed samples, and provide the appropriate predictive intervals. A data example has been provided for illustrative purposes.

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“…Now using the above procedure, a 100(1-α)% credible interval can be obtained as ( θ δ , θ δ+1−α ), for δ = w [1] , w [1] + w [2] , • • • ,…”

Section: Accepted Manuscriptmentioning

confidence: 99%

On Progressively Type-II Censored Two-parameter Rayleigh Distribution

Dey

Dey²,

Kundu

2015

Communications in Statistics - Simulation and Computation

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“…Now we construct a predictive interval for . In symmetric case, the predictive interval for can be obtained by and for the lower bound L and upper bound U respectively, see Al-Jarallah and Al-Hussaini [ 3 ]. While in asymmetric case, the predictive interval of the form and (0, U ) with the coverage probability can be obtained by and for L and U respectively.…”

Section: Bayes Predictionmentioning

confidence: 99%

Statistical Inferences: Based on Exponentiated Exponential Model to Assess Novel Corona Virus (COVID-19) Kerala Patient Data

et al. 2021

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In this article, we use exponentiated exponential distribution as a suitable statistical lifetime model for novel corona virus (covid-19) Kerala patient data. The suitability of the model has been followed by different statistical tools like the value of logarithm of likelihood, Kolmogorov–Smirnov distance, Akaike information criterion, Bayesian information criterion. Moreover, likelihood ratio test and empirical posterior probability analysis are performed to show its suitability. The maximum-likelihood and asymptotic confidence intervals for the parameters are derived from Fisher information matrix. We use the Markov Chain Monte Carlo technique to generate samples from the posterior density function. Based on generated samples, we can compute the Bayes estimates of the unknown parameters and can also construct highest posterior density credible intervals. Further we discuss the Bayesian prediction for future observation based on the observed sample. The Gibbs sampling technique has been used for estimating the posterior predictive density and also for constructing predictive intervals of the order statistics from the future sample.

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“…Table1: Effect of changing hyper parameters on coverage, AW for n = 10 and AC ≈2 b1= b2, a1=a2 Coverage AW (10,10) 0.96 4.90158 (10,40) 0.96 19.75284 (40,10) 0.96 0.98929 (10,70) 0.958 33.67141 (70, 10) 0.962, 0.54693 -As the shape parameter (b) increases while fixing the scale parameter (a) the AW of the prediction interval decreases.…”

Section: Simulation Studymentioning

confidence: 99%

Bayesian Prediction of order statistics based on finite mixture of general class of distributions under Random Censoring

Ismail

Moawad

2019

Pak.j.stat.oper.res.

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This paper focuses on the Bayesian prediction of kth ordered future observations modelled by a two-component mixture of general class of distributions. Samples under consideration are subject to random censoring. A closed form of Bayesian predictive density is obtained under a two-sample scheme. Applications to Weibull and Burr XII components are presented and comparisons with previous results are made. A numerical example is presented for special cases of the exponential and Lomax components to obtain interval prediction of first and last order statistics.

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Bayes inference under a finite mixture of two-compound Gompertz components model

Cited by 8 publications

References 20 publications

On Progressively Type-II Censored Two-parameter Rayleigh Distribution

On Progressively Type-II Censored Two-parameter Rayleigh Distribution

Statistical Inferences: Based on Exponentiated Exponential Model to Assess Novel Corona Virus (COVID-19) Kerala Patient Data

Bayesian Prediction of order statistics based on finite mixture of general class of distributions under Random Censoring

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