Some Functionals and Approximation Operators Associated with a Family of Discrete Probability Distributions (original) (raw)
A new class of discrete distributions
Brazilian Journal of Probability and Statistics, 2009
A new class of discrete distributions is introduced by extending the generalized hypergeometric recast distribution; some of its properties are studied. It is shown that all its moments exist finitely. A genesis, probability mass function, mean and variance are obtained. Certain recurrence relations for probabilities, moments and factorial moments are derived. Certain mixtures and limiting cases are also considered.
A Note on Some -Functions and Their Probability Distributions
2017
Department of Mathematics, University of Sargodha, Sargodha, Pakistan 2 Department of Statistics, University of Agriculture, Faisalabad, Pakistan 4 Department of Mathematics, University of Sargodha, Sargodha, Pakistan E-mail: abdurrehman2007@hotmail.com, rabi.asma6@gmail.com, saba.siddiq112@gmail.com , smjhanda@gmail.com ABSTRACT. In this note, we define some new probability distributions involving a new parameter > 0, named as probability -distributions. We prove some properties of these -distributions which generalize the classical results. Here, we present the moment generating functions of said distributions and establishes the results in terms of Pochhammer -symbol. Also, the authors prove some results showing the link between these distributions.
Characterizations of Three (2020) Introduced Discrete Distributions
2020
The problem of characterizing a probability distribution is an important problem which has attracted the attention of many researchers in the recent years. To understand the behavior of the data obtained through a given process, we need to be able to describe this behavior via its approximate probability law. This, however, requires to establish conditions which govern the required probability law. In other words we need to have certain conditions under which we may be able to recover the probability law of the data. So, characterization of a distribution plays an important role in applied sciences, where an investigator is vitally interested to find out if their model follows the selected distribution. In this short note, certain characterizations of three recently introduced discrete distributions are presented to complete, in some way, the works of Hussain(2020), Eliwa et al.(2020) and Hassan et al.(2020).
A New Method for Generating Discrete Analogues of Continuous Distributions
Journal of Statistical Theory and Applications, 2018
In this paper we use discrete fractional calculus for showing the existence of delta and nabla discrete distributions and then apply time scales for definition of delta and nabla discrete gamma distributions. The main result of this paper is unification of the continuous and discrete gamma distributions, which is at the same time a distribution to so-called time scale. Also, starting from the Laplace transform on time scales, we develop concept of moment generating function for these distributions.
A Generalization to the Family of Discrete Distributions
An alternative approaches for a couple of discrete distributions like Binomial and Multinomial, Poisson, etc having more general form of sampling method (more than one outcome in one trial) compared to tradition sampling heuristics have been suggested and termed as Generalized Binomial, Generalized Multinomial, Generalized Poisson, Generalized Geometric respectively. It is evident that the traditional existing distributions are the special cases of the proposed generalized distributions. The basic distributional properties of the proposed distributions have also been examined including the limiting form. Real life examples are cited for the respective distributions.
Some Approximation Aspects for a New Class Cumulative Distribution Functions
2018
In this paper we introduce and consider a new class of cumulative distribution functions. This class belongs to the important class of functions arising from the theory of impulse techniques, neural networks and debugging theory. By this family we study the Hausdorff approximation of the impulse function σ(t). Numerical examples, illustrating our results using the programming environment CAS MATHEMATICA are presented. AMS Subject Classification: 41A46
Statistics, 2014
A new one-parameter discrete distribution is introduced. Its mathematical properties and estimation procedures are derived. Four real data sets are used to show that the new model performs at least as well as the traditional one-parameter discrete models and other newly proposed two-parameter discrete models.
Classes of Probability Distributions and Their Applications
The aim of this paper is a nontrivial application of certain classes of probability distribution functions with further establishing the bounds for the least root of the functional equation x = b G(µ µx), where b G(s) is the Laplace-Stieltjes transform of an unknown probability distribution function G(x) of a positive random variable having the first two moments g1 and g2, and µ is a positive parameter satisfying the condition µg1 > 1. The addi- tional information characterizing G(x) is that it belongs to the special class of distributions such that the difference between two elements of that class in the Kolmogorov (uniform) metric is not greater than �. The obtained result is then used to establish the lower and upper bounds for loss probabilities in certain loss queueing systems with large buffers as well as continuity theorems in large M/M/1/n queueing systems.
Characterizations of some discrete distributions
We give characterizations of the random variables X i , i=1,2,⋯,m, each X i being independently distributed as generalized Poisson, or as generalized negative binomial distribution. These distributions are characterized by the probability distributions which are generated through the urn models incorporating predetermined strategies.
Preservation of Classes of Discrete Distributions Under Reliability Operations
2016
In this paper we consider some widely utilized classes of discrete distributions and aim to provide a systematic overview about their preservation under convolution. This paper will serve as a detailed reference for the study and applications of the preservation of the discrete NBU(2), NBUCA classes of discrete distributions.
On the discrete analog of gamma-Lomax distribution: properties and applications
arXiv: Statistics Theory, 2018
A two parameter discrete gamma-Lomax distribution is derived as a discrete analogous to the continuous three parameters gamma-Lomax distribution (see Alzaatreh et al. (2013, 2014)) using the general approach for discretization of continuous probability distributions. Some useful structural properties of the proposed distribution are examined. Possible areas of application are also discussed.
Analytic Univalent Functions Defined by Generalized Discrete Probability Distribution
Earthline Journal of Mathematical Sciences, 2020
The close-to-convex analogue of a starlike functions by means of generalized discrete probability distribution and Poisson distribution was considered. Some coefficient inequalities and their connection to classical Fekete-Szego theorem are obtained. Our results provide strong connection between Geometric Function Theory and Statistics.
On a new class of probability distributions
Applied Mathematics Letters, 2011
Multicomponent systems are widely used in computer science. The reliability of these systems plays a very important role in efficient working. These systems are not always supposed to follow the standard probability distributions and so pseudo-distributions can be thought of as suitable alternatives. In this work we have defined a new bivariate pseudo-Weibull distribution. Some standard properties of the distribution have been studied. The distributions of the order statistics and concomitants have also been obtained.
Characterizations of Twenty (2020-2021) Proposed Discrete Distributions
Pakistan Journal of Statistics and Operation Research, 2021
In this paper, certain characterizations of twenty newly proposed discrete distributions: the discrete generalized Lindley distribution of El-Morshedy et al.(2021), the discrete Gumbel distribution of Chakraborty et al.(2020), the skewed geometric distribution of Ong et al.(2020), the discrete Poisson X gamma distribution of Para et al.(2020), the discrete Cos-Poisson distribution of Bakouch et al.(2021), the size biased Poisson Ailamujia distribution of Dar and Para(2021), the generalized Hermite-Genocchi distribution of El-Desouky et al.(2021), the Poisson quasi-xgamma distribution of Altun et al.(2021a), the exponentiated discrete inverse Rayleigh distribution of Mashhadzadeh and MirMostafaee(2020), the Mlynar distribution of Frühwirth et al.(2021), the flexible one-parameter discrete distribution of Eliwa and El-Morshedy(2021), the two-parameter discrete Perks distribution of Tyagi et al.(2020), the discrete Weibull G family distribution of Ibrahim et al.(2021), the discrete Marshall-Olkin Lomax distribution of Ibrahim and Almetwally(2021), the two-parameter exponentiated discrete Lindley distribution of El-Morshedy et al.(2019), the natural discrete one-parameter polynomial exponential distribution of Mukherjee et al.(2020), the zero-truncated discrete Akash distribution of Sium and Shanker(2020), the two-parameter quasi Poisson-Aradhana distribution of Shanker and Shukla(2020), the zero-truncated Poisson-Ishita distribution of Shukla et al.(2020) and the Poisson-Shukla distribution of Shukla and Shanker(2020) are presented to complete, in some way, the authors' works.
Characterizations of Fourteen (2021-2022) Proposed Discrete Distributions
Pakistan Journal of Statistics and Operation Research
As we mentioned in our previous works, sometimes in real life cases, it is very difficult to obtain samples from a continuous distribution. The observed values are generally discrete due to the fact that they are not measured in continuum. In some cases, it may be possible to measure the observations via a continuous scale, however, they may be recorded in a manner in which a discrete model seems more suitable. Consequently, the discrete models are appearing quite frequently in applied fields and have attracted the attention of many researchers. Characterizations of distributions are important to many researchers in the applied fields. An investigator will be vitally interested to know if their model fits the requirements of a particular distribution. To this end, one will depend on the characterizations of this distribution which provide conditions under which the underlying distribution is indeed that particular distribution. Here, we present certain characterizations of 14 recent...
Characterizations of discrete distributions using the
2005
Consider the multivariate splitting model N =N 1 +• • •+N k , where N 1 ,. .. , N k , k 3, are arbitrary (not necessarily independent) random variables (r.v.'s) taking values in N = {0, 1,. . .}, and assume that the Rao-Rubin condition is satisfied for N 1 and N 2. Also assume that the conditional distribution of the vector (N 1 ,. .. , N k) given N is a convolution type. Characterizations related to this model (with k = 2) was first considered by Shanbhag (1977. J. Appl. Probab. 14, 640-646), as an extension of the binomial damage model established by Rao and Rubin (1964. Sankhyā Ser. A 26, 295-298), and was extended to any k 3 by Rao and Srivastava (1979. Sankhyā Ser. A 41, 124-128). In the present paper we provide an alternative set of conditions, under which the distribution of N is characterized, and we apply the result to some discrete distributions.
A new family of distributions based on probability generating functions
Sankhya B, 2011
This paper examines a method for generating new classes of distributions which arise naturally in practice. The generated classes of distributions include the well known Marshall and Olkin class of distributions and can be thought of as mixing two discrete distributions or a discrete distribution with an absolutely continuous distribution. Properties of these classes of distributions are derived and a number of existing results in the literature are recovered as special cases. Finally, failure rates for a special class of distributions which are obtained when the discrete distribution is assumed to have a Harris form are given.