Related papers: Bicomplex Mittag-Leffler Distribution
The Lindley distribution and its numerous generalizations are widely used in statistical and engineering practice. Recently, a power transformation of Lindley distribution, called the power Lindley distribution, has been introduced by M. E.…
An interesting line of research is the investigation of the laws of random variables known as Dirichlet means. However, there is not much information on interrelationships between different Dirichlet means. Here, we introduce two…
Analytical and numerical studies on many-body stochastic processes with multiplicative interactions are reviewed. The method of moment relations is used to investigate effects of asymmetry and randomness in interactions. Probability…
The main purpose of this note is to point out the relevance of the Mittag-Leffler probability distribution in the so-called thinning theory for a renewal process with a queue of power law type. This theory, formerly considered by Gnedenko…
In this article, we study the distribution of values of Dirichlet $L$-functions, the distribution of values of the random models for Dirichlet $L$-functions, and the discrepancy between these two kinds of distributions. For each question,…
The Mittag-Leffler function plays a role of central importance in the theory of fractional derivatives. In this brief note we discuss the properties of this function and its connection with the Wright-Bessel functions and with a new family…
This note corrects a technical error in Guardiola (2020, Journal of Statistical Distributions and Applications), presents updated derivations, and offers an extended discussion of the properties of the spherical Dirichlet distribution.…
In this survey we stress the importance of the higher transcendental Mittag-Leffler function in the framework of the Fractional Calculus. We first start with the analytical properties of the classical Mittag-Leffler function as derived from…
We introduce a compositional framework for convex analysis based on the notion of convex bifunction of Rockafellar. This framework is well-suited to graphical reasoning, and exhibits rich dualities such as the Legendre-Fenchel transform,…
The beta normal distribution is a generalization of both the normal distribution and the normal order statistics. Some of its mathematical properties and a few applications have been studied in the literature. We provide a better foundation…
A class of Laplace transforms is examined to show that particular cases of this class are associated with production-destruction and reaction-diffusion problems in physics, study of differences of independently distributed random variables…
Recently it has been observed that the bivariate generalized linear failure rate distribution can be used quite effectively to analyze lifetime data in two dimensions. This paper introduces a more general class of bivariate distributions.…
An important line of research is the investigation of the laws of random variables known as Dirichlet means as discussed in Cifarelli and Regazzini(1990). However there is not much information on inter-relationships between different…
This paper combines probability theory and fractional calculus to derive a novel integral representation of the three-parameter Mittag-Leffler function or Prabhakar function, where the three parameters are combinations of four base…
The Mittag-Leffler function plays an important role in Geometric Function Theory, particularly in the study of analytic and meromorphic function classes. Among its various generalizations, the Barnes-Mittag-Leffler function stands out due…
For two vast families of mixture distributions and a given prior, we provide unified representations of posterior and predictive distributions. Model applications presented include bivariate mixtures of Gamma distributions labelled as…
Observed clusters should be modelled by considering the distribution function to be a random variable that quantifies the degree of excitation of the system's normal modes. A system of canonical coordinates for the space of DFs is…
We review the function theoretical properties of the Mittag-Leffler function $E_{a,b}\left( z\right) $ in a self-contained manner, but also add new results; more than half is new!
We consider the probability theory, and in particular the moment problem and universality theorems, for random groups of the sort of that arise or are conjectured to arise in number theory, and in related situations in topology and…
In order to describe more complex problem using the concept of fractional derivatives, we introduce in this paper the concept of fractional derivatives with orders. The new definitions are based upon the concept of power law together with…