On an alternative to four notable distribution functions with applications in engineering and the business sciences

Abstract

A new parametric probability distribution function is introduced and its connections with some well-known distribution functions are discussed. Due to its flexibility, we call the novel distribution function the pliant distribution function. We show that the asymptotic pliant probability distribution function can coincide with the Weibull-, exponential and logistic probability distribution functions. Furthermore, we demonstrate that with appropriate parameter settings, the novel distribution gives a simple and accurate approximation to the standard normal probability distribution. Next, we show that the pliant probability distribution function, as an alternative to the Weibull-and exponential distribution functions, can be used to model constant, monotonic and bathtub-shaped hazard functions in reliability theory. We also point out that a function transformed from the new probability distribution function can be applied in the so-called kappa regression analysis method, which may be viewed as an alternative to logistic regression.