A new data analysis method with properties and simulation: Its applications using the radiation, elderly sports and economic data

In the present study, we introduce a new family of probability distributions called the New Flexible Generalized-X family of distributions. Based on this newly developed method, we propose a novel versatile version of the existing Weibull distribution. The newly proposed distribution may be referred to as the New Flexible Generalized Weibull distribution. The probability density and hazard rate functions of the proposed distribution are visually analyzed. The density function of the newly proposed model exhibits positively skewed behavior, and its hazard function also shows a variety of different patterns. The quantile function, moments, moment-generating function, characteristic function, and order statistics of the proposed distribution are derived. Additionally, the actuarial measures, such as VaR (value-at-risk), TVaR (tailed VaR), TV (tailed-variance), and TVP (tailed-variance-premium), are numerically and graphically illustrated to examine the tail patterns of the proposed distribution. The maximum likelihood estimation method is applied to estimate the unknown model parameters of the proposed distribution. Furthermore, a Monte Carlo simulation analysis demonstrates the efficacy of the applied estimation method for the new distribution. The superiority and versatility of the newly introduced distribution are compared with eight well-known existing distributions using five real datasets from the realm of radiation, sports, and economics sectors. Based on these datasets, it is concluded that the newly proposed distribution provides superior fits, both numerically and graphically.