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.

A Notable Bounded Probability Distribution for Environmental and Lifetime Data

“…So we are looking for the robust value of d which will probably be established under the condition that d is greater than the largest element in the sample. Moreover, the convergence of proposed model's MLEs depends upon the huge value of d, i.e., d → ∞ which follows the standard epsilon distribution theory, for more details, the reader is referred toDombi et al (2018),Dombi et al (2019),Dombi and Jónás (2020) andDombi and Jónás (2021).…”

Some Notes on the Omega Distribution and the Pliant Probability Distribution Family

“…Once more it is shown that omega function is asymptotically identical with the exponential function (for more details see ( [20] Theorem 1) and ([21] Proposition 1)). Some probability distributions are founded on this auxiliary function as the omega probability distribution (see [20]) and the pliant probability distribution family (see [21,22]). Hence, some probability distributions, which formulas include exponential terms, also can be approximated using this function, for example, the well-known Weibull, Exponential and Logistic probability distributions.…”

“…In 2020 based on omega function Dombi and Jónás [21] proposed new four-parameter probability distribution function called the pliant probability distribution function (see also ([22] Chapter 3)). Definition 4.…”

“…1, 1, 2, 3, 3, 3, 3, 4, 5, 5, 5, 5, 5, 7, 7, 7, 9, 9, 10,11,11,11,11,12,12,12,12,13,14,14,14,14,14,14,14,14,15,15,15,16,16,16,18,18,18,18,18,18,20,20,21,21,22,22,22,23,23,23,24,24,25,26,26,27,27,29,29,29,29,30,31,31,…”

“…In 2019 Dombi et al [20] (see also [21]) suggested an auxiliary function that is called the omega function.…”