Estimation of Parameters of Generalized Inverted Exponential Distribution for Progressive Type-II Censored Sample with Binomial Removals

Singh, Sanjay Kumar; Singh, Umesh; Kumar, Manoj

doi:10.1155/2013/183652

Cited by 23 publications

(20 citation statements)

References 17 publications

(23 reference statements)

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“…Apart from its usage in Poisson processes, it has been used extensively in the literature for life testing. The Exponential distribution is memoryless and has a constant failure rate; this latter property makes the distribution unsuitable for real life problems with bathtub failure rates (See Singh et al [17] for details) and inverted bathtub failure rates, hence the need to generalize the Exponential distribution in order to increase its flexibility and capability to model some other real life problems. For details about the Exponential distribution, we refer readers to [12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

The Transmuted Inverse Exponential Distribution

Oguntunde¹,

Adejumo²

2014

IJASP

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This article introduces a two-parameter probability model which represents another generalization of the Inverse Exponential distribution by using the quadratic rank transmuted map. The proposed model is named Transmuted Inverse Exponential (TIE) distribution and its statistical properties are systematically studied. We provide explicit expressions for its moments, moment generating function, quantile function, reliability function and hazard function. We estimate the parameters of the TIE distribution using the method of maximum likelihood estimation (MLE). The hazard function of the model has an inverted bathtub shape and we propose the usefulness of the TIE distribution in modeling breast cancer and bladder cancer data sets.

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Section: Introductionmentioning

confidence: 99%

The Transmuted Inverse Exponential Distribution

Oguntunde¹,

Adejumo²

2014

IJASP

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“…Progressively Type-II censored sampling is an important method of obtaining data in such lifetime studies. Singh et al (2013) estimates the parameters of exponentiated Pareto distribution under random removals scheme. Azimi et al (2014) presents some statistical inference for the generalized Pareto distribution based on progressive Type-II censored data with random removals.…”

Section: Progressive Censoring With Random Schemementioning

confidence: 99%

Progressive Censored Burr Type-XII Distribution Under Random Removal Scheme: Some Inferences

Prakash¹

2017

JAS

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Abstract. When some sample values at either or both the extremes might have been assorted, a censoring scheme is much useful. Nevertheless, in some reliability experiments, the number of items fell out the experiment cannot be prefixed random in some situations. For such situations, a random removal scheme with censoring scheme may offer a good result. Here, a random removal scheme with the Progressive censoring plan is assumed for statistical inference, when fill out items of the experiments cannot be prefixed. The analysis of the present discussion has carried out with the help of a real data set for the Burr Type-XII distribution.Résumé. Lorsque certaines valeurs d'échantillonà l'une ou l'autre des deux extrêmes ont puêtre assorties, un schéma de censure est très utile. Néanmoins, dans certaines expériences de fiabilité, le nombre d'articles tombés en panne ne peut pasêtre préfixé. Dans de telles situations, un système de suppression aléatoire avec un système de censure peut offrir un bon résultat. Ici, un système de suppression aléatoire avec un plan de censure progressif est supposé pour l'inférence statistique, lorsque le nombre de pannes ne peutêtre préfixé. L'analyse de la présente discussion aété effectuéeà l'aide d'un ensemble de données réelles issues de la distribution Burr Type-XII.

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“…The marginal posterior PDFs of and are given respectively by [5,7] Note that the above integrals cannot be obtained directly, therefore; we must resort to numerical methods at their evaluation. By using Markov Chain Monte Carlo (MCMC) methods and specially Metropolis-Hasting algorithm to generate random samples from posterior distributions for two the parameters under study in order to be used as Bayesian estimators [6,8] . Posterior distributions can be written as follows:…”

Section: A Joint Posterior Distribution Of and Ismentioning

confidence: 99%

Comparing Bayes estimation with Maximum Likelihood Estimation of Generalized Inverted Exponential Distribution in Case of Fuzzy Data

Al-Kazaz¹,

Al-Saadi²

2017

JEAS

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In this paper, the generalized inverted exponential distribution is considered as one of the most important distributions in studying failure times. A shape and scale parameters of the distribution have been estimated after removing the fuzziness that characterizes its data because they are triangular fuzzy numbers. To convert the fuzzy data to crisp data the researcher has used the centroid method. Hence the studied distribution has two parameters which show a difficulty in separating and estimating them directly of the MLE method. The Newton-Raphson method has been used.For the Bayesian method, the gamma distribution has been proposed as a prior distribution for the two parameters with a quadratic loss function and by using Metropolis-Hasting algorithm to find the Bayesian parameters estimators. Different samples have been generated to represent the population under study by using simulation approach. After estimating the parameters, the results of the two methods have been compared according to the Mean Squared Error measurement. And the researcher concluded that the best estimation method is the MLE followed by the Bayesian.

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Estimation of Parameters of Generalized Inverted Exponential Distribution for Progressive Type-II Censored Sample with Binomial Removals

Cited by 23 publications

References 17 publications

The Transmuted Inverse Exponential Distribution

The Transmuted Inverse Exponential Distribution

Progressive Censored Burr Type-XII Distribution Under Random Removal Scheme: Some Inferences

Comparing Bayes estimation with Maximum Likelihood Estimation of Generalized Inverted Exponential Distribution in Case of Fuzzy Data

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