TRANSMUTED NEW CLASS SINE – G (TNCS-G) FAMILY OF DISTRIBUTION: DISTRIBUTIONAL PROPERTIES AND APPLICATIONS

Abstract

This research introduces a novel family of probability distribution referred to as Transmuted New Class Sine-G (TNCS-G) family of distribution with Transmuted New Class Sine-Weibull (TNS-W) distribution as its sub model. The new TNCS-G family is an extension of the New Class Sine-G Family of Distribution developed by Sapkota (2023). Using the transmutation map, the probability density function (pdf) and the cumulative distribution function (cdf) of the proposed family of distribution and its sub model with weibull distribution as baseline distribution were derived. The Transmuted New Class Sine Weibull (TNCS-W) distribution is developed by combining the transmutation technique with the sine function and the Weibull distribution. Existing Weibull-based models often fail to adequately capture complex behaviours such as skewness, heavy tails, or non-monotonic hazard rates, motivating the need for more flexible models. The objective of this study is to propose and investigate the TNCS-W distribution as a more adaptable model for real-life data. Distributional properties including the probability density function (PDF), cumulative distribution function (CDF), hazard rate function, moments, and quantile function are derived. Parameters are estimated using Maximum Likelihood Estimation (MLE), and the T-SGW is compared with the New Weighted Weibull (NWWD) and standard Weibull distributions using real datasets. Results show that the TNCS-W consistently yields superior fits, as indicated by lower AIC and log-likelihood values (e.g., for rainfall data: AIC = 609.57 for TNCS-W versus 656.28 for NWWD). These findings demonstrate that the TNCS-W provides a more accurate and flexible alternative for applications in fields such as reliability...