PCM Transformation: Properties and Their Estimation

  • Dinesh Kumar Department of Statistics, Banaras Hindu University, Varanasi, India
  • Pawan Kumar Department of Statistics, Banaras Hindu University, Varanasi, India https://orcid.org/0000-0002-6738-7698
  • Pradip Kumar Department of Statistics, Banaras Hindu University, Varanasi, India
  • Sanjay Kumar Singh Department of Statistics, Banaras Hindu University, Varanasi, India
  • Umesh Singh Department of Statistics, Banaras Hindu University, Varanasi, India
Keywords: Maximum likelihood estimator, moment generating function, PCME(θ)-distribution, absolute relative bias (ARB), simulation study.

Abstract

In the present piece of work, we are going to propose a new trigonometry based transformation called PCM transformation. We have been obtained its various statistical properties such as survival function, hazard rate function, reverse-hazard rate function, moment generating function, median, stochastic ordering etc. Maximum Likelihood Estimator (MLE) method under classical approach and Bayesian approaches are tackled to obtain the estimate of unknown parameter. A real dataset has been applied to check its fitness on the basis of fitting criterions Akaike Information criterion (AIC), Bayesian Information criterion (BIC), log-likelihood (-LL) and Kolmogrov-Smirnov (KS) test statistic values in real sense. A simulation study is also being conducted to assess the estimator’s long-term attitude and compared over some chosen distributions.

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Author Biographies

Dinesh Kumar, Department of Statistics, Banaras Hindu University, Varanasi, India

Dinesh Kumar is Assistant Professor of Statistics at Banaras Hindu University. He received the Ph. D. degree in “Statistics” at Banaras Hindu University. He is working on Bayesian Inferences for lifetime models. He is trying to establish some fruitful lifetime models that can cover most of the realistic situations. He also worked as reviewer in different international journals of repute.

Pawan Kumar, Department of Statistics, Banaras Hindu University, Varanasi, India

Dinesh Kumar is Assistant Professor of Statistics at Banaras Hindu University. He received the Ph. D. degree in “Statistics” at Banaras Hindu University. He is working on Bayesian Inferences for lifetime models. He is trying to establish some fruitful lifetime models that can cover most of the realistic situations. He also worked as reviewer in different international journals of repute.

Pradip Kumar, Department of Statistics, Banaras Hindu University, Varanasi, India

Pradip Kumar is a Research Scholar, pursuing Ph.D. at Department of Statistics, Institute of Science, Banaras Hindu University, Varanasi. He started his research in the area of “Bayesian Theory and Reliability Theory” and also developing new distribution with a hope to get much flexible distribution that can fit most of the real data. Currently he is working on Bayesian inferences of Lifetime models.

Sanjay Kumar Singh, Department of Statistics, Banaras Hindu University, Varanasi, India

Sanjay Kumar Singh is Professor & Head, Department of Statistics at Banaras Hindu University. He received the Ph.D. degree in “Statistics” at Banaras Hindu University His main area of interest is Statistical Inference. Presently he is working on Bayesian principle in life testing and reliability estimation, analyzing the demographic data and making projections based on the technique. He also acts as reviewer in different international journals of repute.

Umesh Singh, Department of Statistics, Banaras Hindu University, Varanasi, India

Umesh Singh is Retired Professor of Statistics and Ex-Coordinator of DST-Centre for Interdisciplinary Mathematical Science at Banaras Hindu University. He received the Ph.D. degree in “Statistics” at Rajasthan University. He is referee and Editor of several international journals in the frame of pure and applied Statistics. He is the founder Member of Indian Bayesian Group. He started research with dealing the problem of incompletely specified models. A number of problems related to the design of experiment, life testing and reliability etc. were dealt. For some time, he worked on the admissibility of preliminary test procedures. After some time he was attracted to the Bayesian paradigm. At present his main field of interest is Bayesian estimation for life time models. Applications of Bayesian tools for developing stochastic model and testing its suitability in demography is another field of his interest.

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Published
2021-07-10
Section
Articles