A Novel Approach to Increase the Goodness of Fits with an Application to Real and Simulated Data Sets

In practice, the data sets with extreme values are possible in many fields such as engineering, lifetime analysis, business, and economics. A lot of probability distributions are derived and presented to increase the model flexibility in the presence of such values. The current study also focuses on investigations to derive a new probability model New Flexible Family (NFF) of distributions. The significance of NFF is carried out using the Weibull distribution called New Flexible Weibull distribution or in short NFW. Various mathematical properties of NFW have been discussed including the estimation of parameters and entropy measures. Two real data sets with extreme values and a simulation study have been conducted so as to delineate the importance of NFW. Furthermore, NFW is compared with other existing probability distributions; numerically, it has been observed that the new mechanism of producing the lifetime probability distributions plays a significant role in making predictions about the population than others using the data sets with extreme values.