Transmuted New Weighted Weibull distribution: Some statistical properties and application to survival time data

Abstract

This article introduces a four-parameter probability distribution function derived by introducing an additional parameter to the New Weighted Weibull distribution proposed by[1]. Using the quadratic rank transmutation map (QRTM) introduced by [2], the three-parameter New Weighted Weibull distribution was generalized to its four-parameter variant titled “Transmuted New Weighted Weibull distribution (TNWWD)”. The probability density function (pdf), cumulative distribution function (CDF), hazard rate, and survival function of the TNWWD model were computed and validated. Consequently, some of the mathematical properties of the proposed model were extensively studied and articulated. The parameter(s) of the TNWWD model were estimated using the method of maximum likelihood estimate. The proposed TNWWD model generally outperforms the competing Weibull and New Weighted Weibull distributions in terms of the Akaike information criterion (AIC), consistent Akaike information criterion (CAIC), Bayesian information criterion (BIC), Hannan quin information criterion (HQIC), and related performance measures. By this, the proposed four-parameter probability distribution function is expected to perform better with a real dataset and at all times. A real dataset on survival time was used to demonstrate the practical application of the proposed TNWWD model.