18 papers · ranked by Valyu relevance
Mohd Ghayasuddin, Musharraf Ali, R. B. Paris
In this paper, we introduce and investigate a new extension of the beta function by means of an integral operator involving a product of Bessel-Struve kernel functions. We also define a new extension of the well-known beta distribution, the Gauss hypergeometric function and the confluent hypergeometric function in…
Faten F. Abdulnabi, Hiba F. Al-Janaby, Firas Ghanim
Special Function Theory is used in many mathematical fields to model scientific progress, from theoretical to practical. This helps efficiently analyze the newly expanded Beta class of functions on a complicated domain. We use Mittag-Leffler and Hurwitz Lerch zeta (HLZ) kernels to produce the Beta function using the…
Saiful R. Mondal
We study the log-convexity of the extended beta functions. As a consequence, we establish Turán-type inequalities. The monotonicity, log-convexity, log-concavity of extended hypergeometric functions are deduced by using the inequalities on extended beta functions. The particular cases of those results also give the…
Mehar Chand
The classical beta function B(x, y) is one of the most fundamental special functions, due to its important role in various fields in the mathematical, physical, engineering and statistical sciences. Useful extensions of the classical Beta function has been considered by many authors. In the present paper, our main…
Nabiullah Khan, Talha Usman, Mohd Aman
We aim to introduce a new extension of beta function and to study its important properties. Using this definition, we introduce and investigate new extended hypergeometric and confluent hypergeometric functions. Further, some hybrid representations of this extended beta function are derived which include some well…
Gauhar Rahman, Kottakkaran Sooppy Nisar, Junesang Choi
The Whittaker function and its diverse extensions have been actively investigated. Here we introduce an extension of the Whittaker function by using the known extended confluent hypergeometric function Φp,v and investigate some of its formulas such as integral representations, a transformation formula, Mellin…
Ali Özyapıcı, Yusuf Gürefe, Emine Missirli
The goal of this paper is to extend the classical and multiplicative fractional derivatives. For this purpose, it is introduced the new extended modified Bessel function and also given an important relation between this new function Iυ(q; x) and the confluent hypergeometric function 1F1(α, β, x). Besides, it is used to…
Rabha W. Ibrahim, M. Z. Ahmad, Hiba F. Al-Janaby
Recently, the generalized hypergeometric function is extended by utilizing the Beta function. Based on this type of function, we introduce a new operator in the open unit disk. The present article investigates some subordination and superordination results for certain normalized analytic functions in the open unit…
Karin Meyer
Multivariate estimates of genetic parameters are subject to substantial sampling variation, especially for smaller data sets and more than a few traits. A simple modification of standard, maximum likelihood procedures for multivariate analyses to estimate genetic covariances is described, which can improve estimates by…
Chibueze Ogbonnaya, Simon Preston, Andrew T. A. Wood
We propose a two-parameter bounded probability distribution called the extended power distribution. This distribution on (0, 1) is similar to the beta distribution, however there are some advantages which we explore. We define the moments and quantiles of this distribution and show that it is possible to give an…
Rosihan M. Ali, See Keong Lee, Saiful R. Mondal
This paper studies an extended Bessel function of the form _{a}\mathtt{B}_{b, p, c}x:= \sum _{k=0}^{\infty}\frac{-c^{k}}{k! \Gamma{a k +p+\frac{b+1}{2}}}\biggl \frac{x}{2}\biggr ^{2k+p}. Representation formulations for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts}…
Ahmed M. Gemeay, Waleed Hamoud Alharbi, Alaa R. El-Alosey, Mazyar Ghadiri Nejad
'Mazyar Ghadiri Nejad'] This article suggests a new method to expand a family of life distributions by adding a parameter to the family, increasing its flexibility. It is called the extended Modi-G family of distributions. We derived the general statistical properties of the proposed family. Different methods of…
Kumar P. Mainali, Eric Slud
Analysis of co-occurrence data in ecology and biogeography with traditional indices has led to many problems. In our recent study (19), we revealed the source of the problem that makes the traditional indices fundamentally flawed and completely unreliable, and we further developed a novel metric of association, alpha…
Matthew W. Linakis, Cynthia Van Landingham, Alessandro Gasparini, Matthew P. Longnecker
Meta-analysis poses a challenge when original study results have been expressed in a non-uniform manner, such as when regression results from some original studies were based on a log-transformed key independent variable while in others no transformation was used. Methods of re-expressing regression coefficients to…
Chuliang Song, Muyang Lu, Joseph R. Bennett, Benjamin Gilbert + 2 more
Beta diversity—the variation among community compositions in a region—is a fundamental measure of biodiversity. Despite a diverse set of measures to quantify beta diversity, most measures have posited that beta diversity is maximized when each community has a single distinct species. However, this assumption overlooks…
Govinda Prasad Dhungana, Vijay Kumar, Robert Jeenchen Chen
This study suggested a new four-parameter Exponentiated Odd Lomax Exponential (EOLE) distribution by compounding an exponentiated odd function with Lomax distribution as a generator. The proposed model is unimodal and positively skewed whereas the hazard rate function is monotonically increasing and inverted bathtubs.…
Amelia Carolina Sparavigna
Previous studies (Sparavigna, 2023) have demonstrated the Tsallis q-Gaussian functions suitable for the analysis of Raman spectra. Here we consider two asymmetric forms of them, with the aim of further improving the fitting of Raman spectra. The first asymmetric form, that we are here proposing for the first time, is a…
Alexander Humeniuk, William Glover
We present a library for evaluating multicenter integrals over polarization operators of the form $x^{m_x} y^{m_y} z^{m_z} r^{-k} C(r)$ using Cartesian Gaussian basis functions. $m_x, m_y, m_z \geq 0$, $k > 2$ are integers, while the cutoff function, $C(r)=(1 - e^{-\alpha r^2})^q$, with $\alpha \in \mathbb{R}_{+}$ and…