A characterization of a bivariate distribution by the marginal and the conditional distributions of the same component

1963 ◽  
Vol 15 (1) ◽  
pp. 215-221 ◽  
Author(s):  
V. Seshadri ◽  
G. P. Patil
Keyword(s):  
Bivariate Distribution ◽  
Conditional Distributions

scholarly journals A general stochastic model for bivariate episodes driven by a gamma sequence

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Charles K. Amponsah ◽  
Tomasz J. Kozubowski ◽  
Anna K. Panorska
Keyword(s):  
Stochastic Model ◽  
Joint Distribution ◽  
Pareto Distribution ◽  
Integral Transforms ◽  
Bivariate Distribution ◽  
Conditional Distributions ◽  
General Stochastic Model ◽  
Heavy Tailed ◽  
Discrete Pareto Distribution ◽  
Special Case

AbstractWe propose a new stochastic model describing the joint distribution of (X,N), where N is a counting variable while X is the sum of N independent gamma random variables. We present the main properties of this general model, which include marginal and conditional distributions, integral transforms, moments and parameter estimation. We also discuss in more detail a special case where N has a heavy tailed discrete Pareto distribution. An example from finance illustrates the modeling potential of this new mixed bivariate distribution.

Optimal couplings are totally positive and more

2004 ◽  
Vol 41 (A) ◽  
pp. 321-332 ◽  
Author(s):  
Paul Glasserman ◽  
David D. Yao
Keyword(s):  
Transportation Problem ◽  
Random Variables ◽  
Total Positivity ◽  
Bivariate Distribution ◽  
Discrete Distributions ◽  
Optimal Solutions ◽  
Totally Positive ◽  
Maximal Correlation ◽  
Optimal Coupling

An optimal coupling is a bivariate distribution with specified marginals achieving maximal correlation. We show that optimal couplings are totally positive and, in fact, satisfy a strictly stronger condition we call the nonintersection property. For discrete distributions we illustrate the equivalence between optimal coupling and a certain transportation problem. Specifically, the optimal solutions of greedily-solvable transportation problems are totally positive, and even nonintersecting, through a rearrangement of matrix entries that results in a Monge sequence. In coupling continuous random variables or random vectors, we exploit a characterization of optimal couplings in terms of subgradients of a closed convex function to establish a generalization of the nonintersection property. We argue that nonintersection is not only stronger than total positivity, it is the more natural concept for the singular distributions that arise in coupling continuous random variables.

Optimal couplings are totally positive and more

2004 ◽  
Vol 41 (A) ◽  
pp. 321-332
Author(s):  
Paul Glasserman ◽  
David D. Yao
Keyword(s):  
Transportation Problem ◽  
Random Variables ◽  
Total Positivity ◽  
Bivariate Distribution ◽  
Discrete Distributions ◽  
Optimal Solutions ◽  
Totally Positive ◽  
Maximal Correlation ◽  
Optimal Coupling

An optimal coupling is a bivariate distribution with specified marginals achieving maximal correlation. We show that optimal couplings are totally positive and, in fact, satisfy a strictly stronger condition we call the nonintersection property. For discrete distributions we illustrate the equivalence between optimal coupling and a certain transportation problem. Specifically, the optimal solutions of greedily-solvable transportation problems are totally positive, and even nonintersecting, through a rearrangement of matrix entries that results in a Monge sequence. In coupling continuous random variables or random vectors, we exploit a characterization of optimal couplings in terms of subgradients of a closed convex function to establish a generalization of the nonintersection property. We argue that nonintersection is not only stronger than total positivity, it is the more natural concept for the singular distributions that arise in coupling continuous random variables.

scholarly journals Bivariate Transmuted Burr Distribution: Properties and Application

2021 ◽  
pp. 15-24
Author(s):  
Muhammad Qaiser Shahbaz ◽  
Jumanah Ahmed Darwish ◽  
Lutfiah Ismail Al Turk
Keyword(s):  
Likelihood Estimation ◽  
Real Data ◽  
Bivariate Distribution ◽  
Conditional Distributions ◽  
Conditional Moments ◽  
Data Application ◽  
Burr Distribution ◽  
Rate Functions ◽  
Simultaneous Modeling ◽  
Complex Joint

The bivariate distributions are useful in simultaneous modeling of two random variables. These distributions provide a way of modeling complex joint phenomenon. In this article, a new bivariate distribution is proposed which is known as the bivariate transmuted Burr (BTB) distribution. This new bivariate distribution is extension of the univariate transmuted Burr (TB) distribution to two variables. The proposed  BTB distribution is explored in detail and the marginal and conditional distributions for the distribution are obtained. Joint and conditional moments alongside hazard rate functions are obtained. The maximum likelihood estimation (MLE) for the parameters of the BTB distribution is also done. Finally, real data application of the BTB distribution is given. It is observed that the proposed BTB distribution is a suitable fit for the data used.

Bivariate distributions as saddle points of mutual information

1978 ◽  
Vol 15 (03) ◽  
pp. 523-530
Author(s):  
Geung Ho Kim ◽  
H. T. David
Keyword(s):  
Mutual Information ◽  
Communication Theory ◽  
Marginal Distribution ◽  
Saddle Points ◽  
Bivariate Distribution ◽  
Conditional Distributions ◽  
Bivariate Distributions ◽  
Moment Conditions

Fix a bivariate distribution F on X × Y, considered as a pair (α, {Fx }), where α is a marginal distribution on X and {Fx } is a collection of conditional distributions on Y. For essentially every (β,{Gx }) satisfying a certain pair of moment conditions determined by (α, {F x }), J(β, {F x }) ≦ J(α, {F x }) ≦ J(α, {G x }), where J is mutual information. This relates to two sorts of extremizations of mutual information of relevance to communication theory and statistics.

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