Double Transformation Sin-Exponential Distribution for Modeling Lifetime Data

Abstract

This paper presents a new approach known as double transformation sine-exponential distribution (DT-Sin-E), a multi-processed distribution derived from two-stage transformation of the exponential baseline within a sine-generated context to improve the flexibility of the lifetime and reliability data analysis. Validation of this model proposed was confirmed and the main mathematical features such as the cumulative distribution function, probability density function, survival function, hazard rate function, cumulative hazard function, moments, quantile function, and random generation method were formulated. Eight parameter estimation strategies: maximum likelihood, least squares, weighted least squares, Cramér–von Mises, Anderson–Darling, maximum product of spacings, percentile estimation, and quasi-least squares were used. The Monte Carlo statistical analysis revealed that estimation accuracy increases with increasing size of the sample, but the best method depends on the sample size and the criterion of performance. Regarding the application in the real data field failure-time observations, the proposed model proved to be better than many established competing distributions on information criterion according to the goodness-of-fit measures and the graphical data analysis. These results suggest the DT-Sin-E distribution is an adaptable, efficient model on life data with complex behavior.  The revised theoretical development further establishes stochastic ordering, scale behavior, mean residual life, order-statistic distributions, reliability measures, and Rényi and Shannon entropy representations.