PCM Transformation: Properties and Their Estimation

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.

[1]  M. H. Tahir,et al.  Two-Parameter Logistic-Exponential Distribution: Some New Properties and Estimation Methods , 2020 .

[2]  S. Nadarajah,et al.  Beta trigonometric distributions , 2006 .

[3]  Pushpa L. Gupta,et al.  Modeling failure time data by lehman alternatives , 1998 .

[4]  Ward Whitt,et al.  Asymptotic Analysis of Tail Probabilities Based on the Computation of Moments , 1995 .

[5]  R. K. Sinha.  A Thought on Exotic Statistical Distributions , 2012 .

[6]  Min Xie,et al.  Reliability analysis using an additive Weibull model with bathtub-shaped failure rate function , 1996 .

[7]  Weighted inverted Weibull distribution: Properties and estimation , 2020 .

[8]  Sanjay Kumar Singh.  ESTIMATION OF PARAMETERS AND RELIABILITY FUNCTION OF EXPONENTIATED EXPONENTIAL DISTRIBUTION: BAYESIAN APPROACH UNDER GENERAL ENTROPY LOSS FUNCTION , 2011 .

[9]  The Lindley negative-binomial distribution: Properties, estimation and applications to lifetime data , 2020 .

[10]  Umesh Singh,et al.  Life Time Distributions: Derived from some Minimum Guarantee Distribution , 2017 .

[11]  G. S. Mudholkar,et al.  Exponentiated Weibull family for analyzing bathtub failure-rate data , 1993 .

[12]  David E. Tyler,et al.  Maximum likelihood estimation for the wrapped Cauchy distribution , 1988 .

[13]  Sajid Ali,et al.  THE COMPARISON OF DIFFERENT ESTIMATION METHODS FOR THE PARAMETERS OF FLEXIBLE WEIBULL DISTRIBUTION , 2020 .

[14]  Ronald E. Glaser,et al.  Bathtub and Related Failure Rate Characterizations , 1980 .

[15]  Sajid Ali,et al.  ON THE BAYESIAN ANALYSIS OF EXTENDED WEIBULL-GEOMETRIC DISTRIBUTION , 2019, Journal of Reliability and Statistical Studies.

[16]  Umesh Singh,et al.  Bayes estimators of the reliability function and parameter of inverted exponential distribution using informative and non-informative priors , 2013 .

[17]  Hassan S. Bakouch,et al.  A new class of probability distributions via cosine and sine functions with applications , 2019, Commun. Stat. Simul. Comput..

[18]  Robert King,et al.  A New Class of Transmuted Inverse Weibull Distribution for Reliability Analysis , 2014 .

[19]  Thong Ngee Goh,et al.  A modified Weibull extension with bathtub-shaped failure rate function , 2002, Reliab. Eng. Syst. Saf..

[20]  Sine square distribution: a new statistical model based on the sine function , 2008 .

[21]  M. Aslam,et al.  Bayesian Estimation of Transmuted Weibull Distribution under Different Loss Functions , 2020, Journal of Reliability and Statistical Studies.

[22]  A new class of distribution having decreasing, increasing, and bathtub-shaped failure rate , 2017 .

[23]  Umesh Singh,et al.  A New Method of Proposing Distribution and Its Application to Real Data , 2016 .

[24]  William T. Shaw,et al.  The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map , 2009, 0901.0434.