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About 3,532 papers for “Multinomial distribution”

Multinomial Distribution

Rajan Chattamvelli, Ramalingam Shanmugam · Synthesis lectures on mathematics and statistics · 2020

Cited by 1

Multinomial distribution

Hallin, M., Piegorsch, W., El Shaarawi, A. · Data Archiving and Networked Services (DANS) · 2012

This article briefly summarizes, for the purpose of easy reference, the definition and main properties of multinomial distributions.

Cited by 0

Multinomial Distribution

Daniel Zelterman · Encyclopedia of Biostatistics · 2005

Abstract The multinomial distribution is the generalization of the binomial to more than two dichotomous categorical outcomes. This multivariate discrete distribution describes the joint behavior of frequencies of each of k possible outcomes following n independent trials. The k individual frequencies follow a binomial distribution and are mutually negatively correlated. The probabilities of each of the k outcomes are usually estimated using loglinear models or Bayesian methods. Goodness‐of‐fit and exact tests assess the adequacy of the model to explain the empirical data. These topics are illustrated with an example from genetics.

Cited by 0

Multinomial Distribution

National Cancer Institute · Definitions · 2020

A discreet probability distribution, which is a generalization of the binomial distribution. This distribution models systems in which each trial results in one of a finite set of outcomes with a fixed probability.

Cited by 0Open access

Multinomial Distribution

Catherine Forbes, Merran Evans, Nicholas Anthony John Hastings et al. · 2010

The multinomial variate is a multidimensional generalization of the binomial. The multinomial distribution relates to a set of n-independent trials of this type. Suppose we wish to test the robustness of a complex component of an automobile under crash conditions. The component may be damaged in various ways each with different probabilities. If we wish to evaluate the probability of a particular combination of failures we could apply the multinomial distribution. A useful approximation to the multinomial distribution is the application of the chi-squared distribution to the analysis of contingency tables. This chapter discusses variate relationships and parameter estimation for the multinomial distribution. Controlled Vocabulary Terms control variate; multinomial distribution; probability

Cited by 1

Matrix multinomial distribution

Yuriy Yurchenko · arXiv (Cornell University) · 2021

In this article, we define a matrix multinomial distribution. We prove some properties of the matrix multinomial distribution. We prove that the matrix Poisson distribution can be used as an approximation to the matrix multinomial distribution under certain conditions. We prove that the matrix normal distribution can be used as an approximation to the matrix multinomial distribution under certain conditions.

Cited by 1Open access

Tests in multinomial distribution

Vladimír Holý · Digital Repository (National Repository of Grey Literature) · 2011

In this paper there are at first described classical goodness-of-fit tests - the Pear- son's χ2 test and the log likehood ratio test. The more modern method of testing is the family of statistics based on power divergence which is generalisation of classical statistics. Another type of generalisation is the family of disparity statis- tics which includes beside the family of power divergence also the families BWHD and BWCS. It is demonstrated that all these test statistics have an asymptotic χ2 distribution. In the program R the exact level and exact power can be calculated for individual tests. Hereafter, moments of test statistics can be derived. On the basis of these comparisons there will be shown which test statistics are the most suitable for the goodness-of-fit tests. 1

Cited by 0

Chapter 28: The Multinomial Distribution

Mary C. Meyer · Society for Industrial and Applied Mathematics eBooks · 2019

The multinomial distribution is a generalization of the binomial ideas. We again have independent trials, with probabilities of the outcomes unchanging over trials, but for each trial we have more than two possible outcomes.

Cited by 0

PoissonMultinomial: The Poisson-Multinomial Distribution

Yili Hong, Zhengzhi Lin, Yueyao Wang et al. · 2022

Implementation of the exact, normal approximation, and simulation-based methods for computing the probability mass function (pmf) and cumulative distribution function (cdf) of the Poisson-Multinomial distribution, together with a random number generator for the distribution. The exact method is based on multi-dimensional fast Fourier transformation (FFT) of the characteristic function of the Poisson-Multinomial distribution. The normal approximation method uses a multivariate normal distribution to approximate the pmf of the distribution based on central limit theorem. The simulation method is based on the law of large numbers. Details about the methods are available in Lin, Wang, and Hong (2022) &lt;<a href="https://doi.org/10.1007%2Fs00180-022-01299-0" target="_top">doi:10.1007/s00180-022-01299-0</a>&gt;.

Cited by 1Open access

A Property of the multinomial distribution /

Kesten, Harry, 1931- author., Morse, Norman, author., United States. Air Force. Office of Scientific Research. et al. · The Journal of the Abraham Lincoln Association

Prepared for the United States Air Force Office of Scientific Research, Mathematics Division, by Cornell University, Ithaca, New York, under Contract No. AF 18(600)-331.

Cited by 0Open access

The mode of a multinomial distribution

H. M. Finucan · Biometrika · 1964

The mode of a multinomial distribution Get access H. M. FINUCAN H. M. FINUCAN University College London Search for other works by this author on: Oxford Academic Google Scholar Biometrika, Volume 51, Issue 3-4, December 1964, Pages 513–517, https://doi.org/10.1093/biomet/51.3-4.513 Published: 01 December 1964

Cited by 18

Multinomial Distribution and Ascertainment by Sex

Arjun K. Gupta, S. G. Lindle · Biometrical Journal · 1982

Abstract New ascertainment models taking into account partitioning by sex and without any constraint concerning dominance of alleles are proposed. These originate beginning from two major pathways. The first pathway assumes independence and that the family sizes for both males and females are known. The second pathway assumes dependence and that only the total family size is known. Ascertainment probabilities based on several different types of dependence are found. Results are obtained for incomplete multiple ascertainment.

Cited by 1

Monotonicity Properties of the Multinomial Distribution

Khursheed Alam · The Annals of Mathematical Statistics · 1970

Let $X = (X_1, \cdots, X_k)$ have the multinomial distribution, given by \begin{equation*} \tag{0.1} \operatorname{Pr}\{X = x\} = n!\prod^k_{i=1} (p^{xi}_i/(x_i!))\end{equation*} where $x = (x_1, \cdots, x_k), \sum^k_{i=1} x_i = n$ and $\sum^k_{i=1}p_i = 1$, and let \begin{equation*} \tag{0.2} C(p_1, \cdots, p_m) = \operatorname{Pr}\{X_i \geqq s_i; i = 1, \cdots, m\}\end{equation*} where $\sum^m_{i=1}s_i\leqq n$ and $m \leqq \min (k - 1, n)$. We show that $C(p_1, \cdots, p_m)$ is nondecreasing in $p_i$ for $i = 1, \cdots, m$ and that for $s_i = s_j$, \begin{equation*} \tag{0.3} C(p_1, \cdots, p_m) \leqq C_{ij}(p_1, \cdots, p_m)\quad\text{and}\end{equation*} \begin{equation*} \tag{0.4} C(p_1, \cdots, p_m) \geqq C_{ijt}(p_1, \cdots, p_m)\end{equation*} where $C_{ij}(p_1, \cdots, p_m)$ is obtained from $C(p_1, \cdots, p_m)$ by substituting $p = \frac{1}{2}(p_i + p_j)$ for $p_i$ and $p_j$ and $C_{ijt}(p_1, \cdots, p_m)$ is obtained from $C(p_1, \cdots, p_m)$ by substituting $t$ for $p_i$ and $p_i + p_j - t$ for $p_j$ where $0 \leqq t \leqq \min (p_i, p_j)$. These and similar results are shown. An application of these results to a multiple decision problem is indicated.

Cited by 16Open access