Related papers: Analytical and easily calculated expressions for c…
In this paper we explore the life expectancy limits by based on the stochastic modeling of mortality and applying the first exit or hitting time theory of a stochastic process. The main assumption is that the health state or the "vitality",…
In this paper, the sum of L independent but not necessarily identically distributed (i.n.i.d.) extended $\eta$-$\mu$ variates is considered. In particular, novel expressions for the probability density function and cumulative distribution…
In this paper, we introduce a new extension of the generalized linear failure rate distributions. It includes some well-known lifetime distributions such as extension of generalized exponential and generalized linear failure rate…
We consider estimating the proportion of random variables for two types of composite null hypotheses: (i) the means of the random variables belonging to a non-empty, bounded interval; (ii) the means of the random variables belonging to an…
The Makeham term is a crucial element in mortality modeling, representing a constant additive hazard that addresses background mortality factors unrelated to aging. Widely used in mortality analysis, this term enables the capture of risks…
In this paper, additional properties of the lower gamma functions and the error functions are introduced and proven. In particular, we prove interesting relations between the error functions and Laplace transform.
This paper introduces a five-parameter lifetime model with increasing, decreasing, upside -down bathtub and bathtub shaped failure rate called as the McDonald Gompertz (McG) distribution. This new distribution extend the Gompertz,…
We consider the alternating zeta function and the alternating $L$-function of a graph $G$, and express them by using the Ihara zeta function of $G$. Next, we define a generalized alternating zeta function of a graph, and express the…
Statistical functions such as the moment-generating function, characteristic function, cumulant-generating function, and second characteristic function are cornerstone tools in classical statistics and probability theory. They provide a…
We derive a simple functional equation with two catalytic variables characterising the generating function of 3-stack-sortable permutations. Using this functional equation, we extend the 174-term series to 1000 terms. From this series, we…
The mean residual life function is a key functional for a survival distribution. It has a practically useful interpretation as the expected remaining lifetime given survival up to a particular time point, and it also characterizes the…
Extended geometric distribution is defined and its mixture is characterized by the property of having completely monotone probability sequence. Also, convolution equations and probability generating functions are used to characterize…
We propose a quadrature-based formula for computing the exponential function of matrices with a non-oscillatory integral on an infinite interval and an oscillatory integral on a finite interval. In the literature, existing quadrature-based…
We derive integral representations in terms of the Macdonald functions for the square modulus $s\mapsto | \Gamma ( a + i s ) |^2$ of the Gamma function and its Fourier transform when $a<0$ and $a\not= -1,-2,\ldots $, generalizing known…
Conventional wisdom assumes that the indefinite integral of the probability density function for the standard normal distribution cannot be expressed in finite elementary terms. While this is true, there is an expression for this…
Exponentiated models have been widely used in modeling various types of data such as survival data and insurance claims data. However, the exponentiated composite distribution models have not been explored yet. In this paper, we introduce…
We introduce a general class of continuous univariate distributions with positive support obtained by transforming the class of two-piece distributions. We show that this class of distributions is very flexible, easy to implement, and…
The Hoover index is a widely used measure of inequality with an intuitive interpretation, yet little is known about the finite-sample properties of its empirical estimator. In this paper, we derive a simple expression for the expected value…
We calculate some infinite sums containing the digamma function in closed-form. These sums are related either to the incomplete beta function or to the Bessel functions. The calculations yield interesting new results as by-products, such as…
Choice functions constitute a simple, direct and very general mathematical framework for modelling choice under uncertainty. In particular, they are able to represent the set-valued choices that appear in imprecise-probabilistic decision…