Topp-Leone Cauchy Family of Distributions with Applications in Industrial Engineering

The goal of this research is to create a new general family of Topp-Leone distributions called the Topp-Leone Cauchy Family (TLC), which is exceedingly versatile and results from a careful merging of the Topp-Leone and Cauchy distribution families. Some of the new family's theoretical properties are investigated using specific results on stochastic functions, quantile functions and associated measures, generic moments, probability weighted moments, and Shannon entropy. A parametric statistical model is built from a specific member of the family. The maximum likelihood technique is used to estimate the model's unknown parameters. Furthermore, to emphasize the new family's practical potential, we applied our model to two real-world data sets and compared it to existing rival models.