scholarly journals Theorizing Probability Distribution in Applied Statistics

2020 ◽  
Vol 1 (1) ◽  
pp. 79-95
Author(s):  
Indra Malakar
Keyword(s):  
Probability Distribution ◽  
Normal Distribution ◽  
Poisson Distribution ◽  
Binomial Distribution ◽  
Identical Condition ◽  
Random Variable ◽  
Fixed Number ◽  
Theoretical Knowledge ◽  
Applied Statistics ◽  
Discrete Random Variable

This paper investigates into theoretical knowledge on probability distribution and the application of binomial, poisson and normal distribution. Binomial distribution is widely used discrete random variable when the trails are repeated under identical condition for fixed number of times and when there are only two possible outcomes whereas poisson distribution is for discrete random variable for which the probability of occurrence of an event is small and the total number of possible cases is very large and normal distribution is limiting form of binomial distribution and used when the number of cases is infinitely large and probabilities of success and failure is almost equal.

Probability and distributions

2020 ◽  
pp. 243-280
Author(s):  
Janet L. Peacock ◽  
Philip J. Peacock
Keyword(s):  
Probability Distribution ◽  
Normal Distribution ◽  
Poisson Distribution ◽  
Binomial Distribution ◽  
Probability Distributions ◽  
Medical Statistics

Probability and probability distributions play a central part in medical statistics. This chapter defines what is meant by probability and describes the rules by which probabilities are combined. It then describes how the use of probability leads to the concept of a probability distribution and shows how these distributions are used in medical statistics. Examples are given of the use of key distributions: the Normal distribution, the binomial distribution, and the Poisson distribution.

scholarly journals A note on characteristic function for Bernstein polynomials involving special numbers and polynomials

Filomat ◽  
2020 ◽  
Vol 34 (2) ◽  
pp. 543-549
Author(s):  
Buket Simsek
Keyword(s):  
Characteristic Function ◽  
Binomial Distribution ◽  
Bernstein Polynomials ◽  
Random Variable ◽  
Stirling Numbers ◽  
Bernoulli Numbers ◽  
Discrete Random Variable ◽  
Euler Numbers ◽  
Negative Order ◽  
Special Numbers And Polynomials

The aim of this present paper is to establish and study generating function associated with a characteristic function for the Bernstein polynomials. By this function, we derive many identities, relations and formulas relevant to moments of discrete random variable for the Bernstein polynomials (binomial distribution), Bernoulli numbers of negative order, Euler numbers of negative order and the Stirling numbers.

A Simple Modification of the Binomial Distribution

1960 ◽  
Vol 15 (06) ◽  
pp. 436-444
Author(s):  
S. W. Dharmadhikari
Keyword(s):  
Probability Distribution ◽  
Poisson Distribution ◽  
Binomial Distribution ◽  
Probability Distributions ◽  
Simple Modification ◽  
Type Iii

Given any probability distribution, new distributions can be derived from it by assuming its parameters to follow some specific probability distributions. A simple example of this process is provided by the Poisson distributionP(r∣λ) =e-λλr/r! (r= o, 1, 2, …).If the parameterλis assumed to follow the Pearson's Type III lawthen the probability ofrsuccesses is obtained as

Some characterizations for the Poisson distribution starting with a power-series distribution

1972 ◽  
Vol 71 (3) ◽  
pp. 517-522 ◽  
Author(s):  
D. N. Shanbhag ◽  
R. M. Clark
Keyword(s):  
Power Series ◽  
Poisson Distribution ◽  
Random Variable ◽  
Discrete Random Variable ◽  
Power Series Distribution ◽  
Destructive Process ◽  
Image Position

Let X be a non-negative discrete random variable with distribution {Px} and Y be a random variable denoting the undestroyed part of the random variable X when it is subjected to a destructive process such that

scholarly journals Analysis of the folded normal distribution of a random variable

2021 ◽  
pp. 111-122
Author(s):  
Степан Алексеевич Рогонов ◽  
Илья Сергеевич Солдатенко
Keyword(s):  
Probability Distribution ◽  
Analytical Solution ◽  
Normal Distribution ◽  
Random Variables ◽  
Random Variable ◽  
Point Of View ◽  
Practical Solution ◽  
Absolute Value ◽  
Actual Error ◽  
Folded Normal Distribution

Анализ поведения случайных величин после различных преобразований можно применять при решении многих нетривиальных задач. В частности, решения, которые невозможно выразить аналитически, с точки зрения практической применимости способны давать результаты с точностью, достаточной для вычислений, вынося невыразимую невязку аналитического решения далеко за рамки требуемой погрешности. В настоящей работе исследовано поведение модуля нормально распределенной случайной величины и выяснено, при каких условиях можно пренебречь операцией взятия абсолютного значения и аппроксимировать модуль случайной величины {\it похожим} распределением вероятностей. The analysis of the behavior of random variables after various transformations can be used in the practical solution of many non-trivial problems. In particular, solutions that cannot be expressed purely analytically, from the point of view of practical applicability, are able to give results with accuracy sufficient for real calculations, taking the inexpressible discrepancy of the analytical solution far beyond the actual error. In this paper, the behavior of the modulus of a normally distributed random variable is investigated and it is found out under what conditions it is possible to neglect the operation of taking an absolute value and approximate the modulus of a random variable with a {\it similar} probability distribution.

scholarly journals Kurtosis

Psychology ◽  
2021 ◽  
Author(s):  
Zhiyong Zhang ◽  
Wen Qu
Keyword(s):  
Probability Distribution ◽  
Normal Distribution ◽  
Random Variables ◽  
Random Variable ◽  
Quantitative Psychology ◽  
Psychometric Models ◽  
Univariate Distribution

In statistics, kurtosis is a measure of the probability distribution of a random variable or a vector of random variables. As mean measures the centrality and variance measures the spreadness of a probability distribution, kurtosis measures the tailedness of the distribution. Kurtosis for a univariate distribution was first introduced by Karl Pearson in 1905. Kurtosis, together with skewness, is widely used to quantify the non-normality—the deviation from a normal distribution—of a distribution. In psychology, kurtosis has often been studied in the field of quantitative psychology to evaluate its effects on psychometric models.

scholarly journals A Simple Method for Generation of Statistical Tables by the Help of Excel Software

2011 ◽  
Vol 2 (1) ◽  
pp. 38-50
Author(s):  
Muhammad Irfan
Keyword(s):  
Normal Distribution ◽  
Poisson Distribution ◽  
Binomial Distribution ◽  
Standard Normal Distribution ◽  
Inverse Transformation ◽  
Chi Square ◽  
Easy Method ◽  
Simple Method ◽  
Standard Normal ◽  
F Distribution

A simple and easy method is employed to construct complete statistical tables like Student’s tdistribution, F distribution, Chi-square distribution and Cumulative standard normal distribution in Excel software which are used in all fields of research. Also, we generate other statistical tables like Cumulative binomial distribution, Cumulative Poisson distribution, Fisher transformation and Fisher inverse transformation. The proposed method depends only on the Excel software; it does not depend on the traditional statistical tables.

Peluang, Peubah Acak Diskrit, dan Sebaran Peluang Peubah Acak Diskrit

2020 ◽  
Author(s):  
Ahmad Sudi Pratikno
Keyword(s):  
Probability Distribution ◽  
Random Variables ◽  
Random Variable ◽  
Discrete Random Variable ◽  
Discrete Random Variables

Probability to learn someone's chance in getting or winning an event. In the discrete random variable is more identical to repeated experiments, to form a pattern. Discrete random variables can be calculated as the probability distribution by calculating each value that might get a certain probability value.

scholarly journals A note on negative λ-binomial distribution

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yuankui Ma ◽  
Taekyun Kim
Keyword(s):  
Explicit Expression ◽  
Binomial Distribution ◽  
Random Variable ◽  
Discrete Random Variable ◽  
Binomial Random Variable

Abstract In this paper, we introduce one discrete random variable, namely the negative λ-binomial random variable. We deduce the expectation of the negative λ-binomial random variable. We also get the variance and explicit expression for the moments of the negative λ-binomial random variable.

On a family of q-binomial distributions

2014 ◽  
Vol 64 (2) ◽  
Author(s):  
Martin Zeiner
Keyword(s):  
Normal Distribution ◽  
Poisson Distribution ◽  
Binomial Distribution ◽  
Convergence Properties ◽  
Basic Properties ◽  
Binomial Distributions ◽  
Convergence Results ◽  
Discrete Normal Distribution

AbstractWe introduce a family of q-analogues of the binomial distribution, which generalises the Stieltjes-Wigert-, Rogers-Szegö-, and Kemp-distribution. Basic properties of this family are provided and several convergence results involving the classical binomial, Poisson, discrete normal distribution, and a family of q-analogues of the Poisson distribution are established. These results generalize convergence properties of Kemp’s-distribution, and some of them are q-analogues of classical convergence properties.

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