Related papers: Analytical and easily calculated expressions for c…
The primary goal of this paper is to introduce and investigate generalized incomplete exponential functions with matrix parameters. Integral representation, differential formula, addition formula, multiplication formula, and recurrence…
In this paper, we suggest a novel method for detecting mortality deceleration. We focus on the gamma-Gompertz frailty model and suggest the subtraction of a penalty in the log-likelihood function as an alternative to traditional likelihood…
We construct asymptotic expansions for the normalised incomplete gamma function $Q(a,z)=\Gamma(a,z)/\Gamma(a)$ that are valid in the transition regions, including the case $z\approx a$, and have simple polynomial coefficients. For Bessel…
The signature of a path can be described as its full non-commutative exponential. Following T. Lyons we regard its expectation, the expected signature, as path space analogue of the classical moment generating function. The logarithm…
We give asymptotic expressions for the number of commuting matrices over finite fields. For this, we use product expansions for the corresponding generating functions.
Generating functions and functional equations of Dickson polynomials of the first and second kind are derived and continued analytically. These formulae are expressed in terms of the incomplete gamma function over complex variables of the…
The limitations resulting from the dichtomisation of continuous outcomes have been extensively described. But the need to present results based on binary outcomes in particular in health science remains. Alternatives based on the…
The simple (linear) birth-and-death process is a widely used stochastic model for describing the dynamics of a population. When the process is observed discretely over time, despite the large amount of literature on the subject, little is…
The generalized Marcum functions appear in problems of technical and scientific areas such as, for example, radar detection and communications. In mathematical statistics and probability theory these functions are called the noncentral…
We show that many important convex matrix functions can be represented as the partial infimal projection of the generalized matrix fractional (GMF) and a relatively simple convex function. This representation provides conditions under which…
In 2021, Hu and Kim defined a new type of gamma function $\widetilde{\Gamma}(x)$ from the alternating Hurwitz zeta function $\zeta_{E}(z,x)$, and obtained some of its properties. In this paper, we shall further investigate the function…
An analysis of the zeta and gamma function is presented, using elementary functions like [] and {}, a general formula for the angle of zeta(1/2 + i*n) is found and the same for the gamma function.
We discuss the best methods available for computing the gamma function $\Gamma(z)$ in arbitrary-precision arithmetic with rigorous error bounds. We address different cases: rational, algebraic, real or complex arguments; large or small…
Gamma process has been extensively used to model monotone degradation data. Statistical inference for the gamma process is difficult due to the complex parameter structure involved in the likelihood function. In this paper, we derive a…
In this paper we propose a new lifetime model, called the odd generalized exponential gompertz distribution, We obtain some of its mathematical properties. Some structural properties of the new distribution are studied. The method of…
We derive product and series representations of the gamma function using Newton interpolation series. Using these identities, a new formula for the coefficients in the Taylor series of the reciprocal gamma function is found. We also find…
In this paper, we investigate the complete monotonicity of some functions involving gamma function. Using the monotonic properties of these functions, we derived some inequalities involving gamma and beta functions. Such inequalities…
In this paper, a new three-parameter lifetime distribution is introduced and many of its standard properties are discussed. These include shape of the probability density function, hazard rate function and its shape, quantile function,…
The expansion of Kummer's hypergeometric function as a series of incomplete Gamma functions is discussed, for real values of the parameters and of the variable. The error performed approximating the Kummer function with a finite sum of…
Distribution functions for random variables that depend on a parameter are computed asymptotically for ensembles of positive Hermitian matrices. The inverse Fourier transform of the distribution is shown to be a Fredholm determinant of a…