# On the Generalized Odd Transmuted Two-Sided Class of Distributions

## DOI:

https://doi.org/10.6092/issn.1973-2201/10427## Keywords:

Hazard rate function, Survival function, Maximum likelihood estimation, Odd ratio function, Regression## Abstract

In this paper, a general class of two-sided lifetime distributions is introduced via odd ratio function, the well-known concept in survival analysis and reliability engineering. Some statistical and reliability properties including survival function, quantiles, moments function, asymptotic and maximum likelihood estimation are provided in a general setting. A special case of this new family is taken up by considering the exponential model as the parent distribution. Some characteristics of this specialized model and also a discussion associated with survival regression are provided.

A simulation study is presented to investigate the bias and mean square error of the maximum likelihood estimators. Moreover, two examples of real data sets are studied; point and interval estimations of all parameters are obtained by maximum likelihood and bootstrap (parametric and non-parametric) procedures. Finally, the superiority of the proposed model over some common statistical distributions is shown through the different criteria for model selection including loglikelihood values, Akaike information criterion and Kolmogorov-Smirnov test statistic values.

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*Statistica*,

*80*(4), 439–467. https://doi.org/10.6092/issn.1973-2201/10427

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