Some Comments on Increasing Modelling Efficiency of Weibull Distribution

Obtaining new statistical distributions involves employing various techniques aimed at enhancing modeling efficiency. In this particular study, a novel distribution is introduced by extracting the conditional diagonal section from the bivariate Farlie-Gumbel-Morgenstern distribution, where the marginals follow the Weibull distribution. The characteristics and specifications of this newly proposed distribution are thoroughly examined. Statistical discussions are held regarding the structure of the distribution, and parameter estimation techniques are applied using established methods. Furthermore, reliability analysis is conducted to assess its performance. To gauge the effectiveness of this innovative distribution for statistical modeling, data sets sourced from existing literature are utilized. Based on the findings, it is deduced that this fresh approach offers an efficient and robust model specifically suited for analyzing lifetime datasets. With this methodology, according to Kolmogorov Smirnov test statistics, the modeling efficiency of the Weibull distribution is increased by more than 20% in some situations.