Estimating Discrete Joint Probability Distributions for Demographic Characteristics at the Store Level Given Store Level Marginal Distributions and a City-Wide Joint Distribution

2005 ◽  
Vol 3 (1) ◽  
pp. 71-93 ◽  
Author(s):  
Charles J. Romeo
Keyword(s):  
Joint Distribution ◽  
Probability Distributions ◽  
Joint Probability ◽  
Demographic Characteristics ◽  
Marginal Distributions ◽  
Joint Probability Distributions

Inferring the Distribution of the Parameters of the von Bertalanffy Growth Model from Length Moments

1988 ◽  
Vol 45 (10) ◽  
pp. 1779-1788 ◽  
Author(s):  
Robert L. Burr
Keyword(s):  
Growth Model ◽  
Joint Distribution ◽  
Probability Distributions ◽  
Joint Probability ◽  
Future Research ◽  
Parameter Estimates ◽  
Von Bertalanffy ◽  
Animal Populations ◽  
Von Bertalanffy Growth Model ◽  
Joint Probability Distributions

A theoretical approach is described for determining the joint distribution of the parameters of the von Bertalanffy growth model from statistical moments of length. The approach extends the work of K. J. Sainsbury, who had demonstrated that different mean parameter estimates are obtained by assuming that the von Bertalanffy equation applies to individual fish rather than to groups of fish. Sainsbury articulated the goal of studying the joint probability distributions of K and L∞ in animal populations and developed a maximum likelihood procedure for estimating the parameters of particular distributional forms describing K and L∞, which were assumed for mathematical convenience to be statistically independent. The primary goal of the present paper is to provide a framework for future research in generalizing Sainsbury's approach by considering (K, L∞) to be a random vector described by a joint probability density function and by allowing broader classes of distributions to be considered. Minimum cross-entropy (MCE) inversion, an information–theoretic methodology for approximating probability distributions, is shown to be effective in selecting a reasonable and unique joint distribution corresponding to observable length moments. Appealing features of the MCE methodology include the ability to include prior knowledge of uncertain applicability and the capacity of the resulting approximate distribution to represent potential stochastic dependencies between the von Bertalanffy parameters. Several numerical examples, using simulated and historical data, are presented to illustrate how information about the variation and covariation of L∞ and K can be inferred from a minimal set of length moments. The directions developed in this paper are far from a practical and useful methodology. The MCE inversion procedure is a "method of moments," with no statistical assessment of reliability. Further research is needed to make this promising pdf approximation scheme better suited for real fisheries problems.

CHECKERBOARD COPULAS OF MAXIMUM ENTROPY WITH PRESCRIBED MIXED MOMENTS

2018 ◽  
Vol 107 (3) ◽  
pp. 302-318
Author(s):  
JONATHAN BORWEIN ◽  
PHIL HOWLETT
Keyword(s):  
Probability Distribution ◽  
Maximum Entropy ◽  
Probability Distributions ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Marginal Distributions ◽  
Joint Probability Distributions

In modelling joint probability distributions it is often desirable to incorporate standard marginal distributions and match a set of key observed mixed moments. At the same time it may also be prudent to avoid additional unwarranted assumptions. The problem is to find the least ordered distribution that respects the prescribed constraints. In this paper we will construct a suitable joint probability distribution by finding the checkerboard copula of maximum entropy that allows us to incorporate the appropriate marginal distributions and match the nominated set of observed moments.

scholarly journals A Consistent Track-to-Track Fusion Method Based on Copula Theory

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Kelin Lu ◽  
K. C. Chang ◽  
Rui Zhou
Keyword(s):  
Probability Distributions ◽  
A Priori ◽  
Joint Probability ◽  
Network Connectivity ◽  
Consistent Estimate ◽  
Fusion Algorithm ◽  
Copula Theory ◽  
Wide Range ◽  
Primary Advantage ◽  
Joint Probability Distributions

This paper addresses the problem of distributed fusion when the conditional independence assumptions on sensor measurements or local estimates are not met. A new data fusion algorithm called Copula fusion is presented. The proposed method is grounded on Copula statistical modeling and Bayesian analysis. The primary advantage of the Copula-based methodology is that it could reveal the unknown correlation that allows one to build joint probability distributions with potentially arbitrary underlying marginals and a desired intermodal dependence. The proposed fusion algorithm requires no a priori knowledge of communications patterns or network connectivity. The simulation results show that the Copula fusion brings a consistent estimate for a wide range of process noises.

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