A New Generalized Two-Sided Class of the Distributions Via New Transmuted Two-Sided Bounded Distribution

Abstract

In the present paper, we first consider a generalization of the standard two-sided power distribution so-called the transmuted two-sided distribution, and then extend proposed idea to generalized two-sided class of distributions, introduced by Korkmaz and Genç [1]. Some statistical and reliability properties including explicit expressions for quantiles, hazard rate function, order statistics, and maximum likelihood estimation are obtained in general setting. Generalized transmuted two-sided exponential distribution is considered as a especial case and denoted with the name TTSG−G. A simulation study is presented to investigate the bias and mean square error of the maximum likelihood estimators. We use a real data set and obtain the maximum likelihood and parametric bootstrap estimator of the parameters of TTSG−G distribution. Finally, the superiority of the new model to some common statistical distributions is shown through the different criteria of selection model including log-likelihood values, Akaike information criterion, and Kolmogorov–Smirnov test statistic values.

Keywords

• Hazard rate function
• order statistics
• maximum likelihood estimator
• transmutation map
• transmuted two-sided distribution