DEVELOPING THE ODD BURR III–BURR III (OBIII–BIII) DISTRIBUTION: THEORETICAL FOUNDATIONS AND APPLICATIONS TO SURVIVAL DATA

Abstract

The normal, exponential, gamma, Dagum, and Burr distributions are commonly used to model uni-modal datasets. While the Burr III distribution is widely applied in reliability and income modeling, it is limited by its inherently decreasing hazard rate, inability to analyze complex survival datasets, bathtub shape hazard rates and asymmetric datasets, which makes it unsuitable for multimodal observations, hence the need to extend the classical Burr III distribution. In response, the study introduced the modified form of Burr III distribution called Odd Burr III-Burr III distribution with four parameters. The new distribution has the ability to capture various data behaviors, including heavy tails, skewness other shapes that the conventional Burr III distribution can’t captured. The probability density function (PDF) and cumulative distribution function (CDF) of the propose model were derived and Log-likelihood function were also sorted out, the goodness of fit and information criteria were adapted to assess the performance of the proposed model using simulated data and real-life applications.