Modification Of Dal Distribution: A Comparative Analysis Of Burr Xii-Dal And Weibull-Dal Distributions

Classical distributions such as Burr-G and Weibull-G distributions with less than four parameters are commonly used to represent lifetime data, frequently prove insufficient in accurately describing real observations. These distributions often struggle to capture
the complexities and nuances present in the data, leading to inaccuracies in modeling and analysis. Hence, this study introduces two new lifetime models based on the aforementioned distributions to address these issues. These models, called BurrXIIDAL and Weibull-DAL, are based on the properties of the DAL distribution, and have five parameters. Statistical analyses are conducted on these models, including examining their reliability properties and density expansion. Their ordinary and incomplete moments, moment generating function, quantile function, probability weighted moments, order statistics, and Renyi entropy have all been derived explicitly. Maximum likelihood technique is used to provide estimates for the model’s parameter using Iterative Broyden-Flether-Goldfrab-Shanno method in the R-package. Then, five
actual datasets are used to demonstrate the ability of the BurrXII-DAL and Weibull- DAL models. Various measures of goodness-of-fit, including AIC, BIC, A*, W* and p-value (KS) are used. Both models, BurrXII-DAL and Weibull-DAL distributions performed better as they are flexible fit to the real data as compared to the other competitive models. The models are proven effective since the prediction of the failure rate is more accurate and the hazard rate function shows flexibility with complicated scenario. BurrXII-DAL and Weibull-DAL distributions with five parameters are successfully developed in this study. This research has provided insights into the strengths and weaknesses of each distribution and has identified situations where one distribution may be more appropriate than the other.