A New Family of Lifetime Models: Theoretical Developments with Applications in Biomedical and Environmental Data

Abstract

With the aim of identifying a probability model that not only correctly describes the stochastic behavior of extreme environmental factors such as excess rain, acid rain pH level, and concentrations of ozone, but also measures concentrations of NO2 and leads deliberations, etc., for a specific site or multiple site forms as well as for life testing experiments, we introduced a novel class of distributions known as the Sine Burr X−G family. Some exceptional prototypes of this class are proposed. Statistical assets of the presented class, such as density function, complete and incomplete moments, average deviation, and Lorenz and Bonferroni graphs, are proposed. Parameter estimation is made via the likelihood method. Moreover, the application is explained by using four real data sets. We have also illustrated the significance and elasticity of the proposed class in the above-mentioned stochastic phenomenon.

Parametric Distributions for Survival and Reliability Analyses, a Review and Historical Sketch

“…The case of δ = 1 is the Pareto type II (Lomax) distribution (Table 1). The Burr XII distribution has been the basis of generating many lifetime distributions, such as the beta Burr XII distribution [89] and the Sine Burr distribution [90]. The Burr XII distribution has been applied to a number of applications, such as the multicomponent stress-strength reliability [91] and disease data analysis with competing risks [92,93].…”