TRANSMUTED SINE GENERALIZED EXPONENTIAL DISTRIBUTION: DISTRIBUTIONAL PROPERTIES AND APPLICATIONS

Abstract

This research paper introduces a novel probability distribution called the Transmuted Sine Generalized-Exponential (T-SGEx) distribution, which is developed by combining the transmutation technique with the sine function and the Generalized-Exponential distribution. The distribution is designed to offer greater flexibility in modeling real-life data, particularly for datasets exhibiting complex behaviors such as skewness, heavy tails, or multimodal patterns. To understand the properties of the T-SGEx distribution, several distributional characteristics, including probability density function (PDF), cumulative distribution function (CDF), hazard rate function, moments, and quantile function, were examined. The study also explored the reliability properties of the distribution, which are critical for applications in survival analysis and engineering.

The estimation of the T-SGEx distribution parameters was performed using Maximum Likelihood Estimation (MLE). Real-life datasets from two previous studies were used to evaluate the performance of the T-SGEx distribution. The goodness-of-fit of the T-SGEx distribution was compared with two competing distributions: the New Weighted Exponential Distribution (NWED) and the standard Exponential Distribution (ED). Model comparison was conducted using the Akaike Information Criterion (AIC) and the negative log-likelihood (NLL). The results demonstrated that the T-SGEx distribution provides a superior fit to the datasets, as evidenced by lower AIC and NLL values compared to the NWE and Exponential distributions.

The findings of this study highlight the practical application of the T-SGEx distribution in modeling real-life data, particularly in fields such as reliability engineering, survival analysis, and environmental studies.

Keywords:  Distribution, Quadratic rank transmutation map, Maximum likelihood estimation, Order Statistics, Transmuted Sine-G distribution