Abstract
A novel two-parameter continuous lifespan model is developed, based on a truncated Fréchet produced family of distributions known as the truncated Fréchet inverted Lindley distribution. It includes a thorough discussion of statistical features such as the quantile function, moments, order statistics, incomplete moments, and Lorenz and Bonferroni curves. The greatest likelihood approach for estimating population parameters is described. Finally, one real-world data set to application is utilized to demonstrate the new distribution’s utility. The data represent the tensile strength, measured in GPa, of 69 carbon fibers tested under tension at gauge lengths of 20 mm.
Highlights
Adding parameter(s) to baseline distributions is a traditional approach for generating families of probability distributions
Ese families have the capacity to increase the desirable aspects of probability distributions as well as extract additional information from a variety of data sets, which may be used in a variety of fields such as engineering, economics, biology, and environmental sciences
If Z ∼ TIITFILi, the median M of Z is given by Q(u) − 1 + θ1 + 1θW− 1− (1 + θ)e− (1+θ)1 − [ln(2e)](− 1/b)− 1. (21)
Summary
Adding parameter(s) to baseline distributions is a traditional approach for generating families of probability distributions. Ese families have the capacity to increase the desirable aspects of probability distributions as well as extract additional information from a variety of data sets, which may be used in a variety of fields such as engineering, economics, biology, and environmental sciences. Another generator utilizes the shortened random variable. E TIIFILi distribution function, the hazard rate function (hrf ), the inverted hazard rate function, and the cumulative hazard rating function are given when a random variable Z follows the TIIFILi model,.
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