On Joint Distribution of Random Variables with Given Cross Conditional Distributions: Discrete Case

1992 ◽  
Vol 36 (2) ◽  
pp. 371-375
Author(s):  
B. M. Gurevich
Keyword(s):  
Joint Distribution ◽  
Random Variables ◽  
Discrete Case ◽  
Conditional Distributions

Characterizations via conditional distributions

1977 ◽  
Vol 14 (04) ◽  
pp. 806-816
Author(s):  
Robert H. Berk
Keyword(s):  
Order Statistics ◽  
Conditional Distribution ◽  
Joint Distribution ◽  
Exponential Family ◽  
Random Variables ◽  
Independent Random Variables ◽  
Conditional Distributions

For independent random variablesXandY,if the conditional distribution ofXgivenX+Ysatisfies certain conditions, then the joint distribution ofXandYis a member of a certain one-parameter exponential family. Extensions fornindependent random variables are given. A characterization for independent random variables involving order statistics is also given.

scholarly journals A Variant of the Necessary Condition for the Absolute Continuity of Symmetric Multivariate Mixture

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1505
Author(s):  
Evgeniy Anatolievich Savinov
Keyword(s):  
Absolute Continuity ◽  
Joint Distribution ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Independent Random Variables ◽  
Necessary Condition ◽  
Conditional Distributions ◽  
One Dimensional ◽  
The Absolute

Sufficient conditions are given under which the absolute continuity of the joint distribution of conditionally independent random variables can be violated. It is shown that in the case of a dimension n>1 this occurs for a sufficiently large number of discontinuity points of one-dimensional conditional distributions.

Characterizations via conditional distributions

1977 ◽  
Vol 14 (4) ◽  
pp. 806-816 ◽  
Author(s):  
Robert H. Berk
Keyword(s):  
Order Statistics ◽  
Conditional Distribution ◽  
Joint Distribution ◽  
Exponential Family ◽  
Random Variables ◽  
Independent Random Variables ◽  
Conditional Distributions

For independent random variables X and Y, if the conditional distribution of X given X + Y satisfies certain conditions, then the joint distribution of X and Y is a member of a certain one-parameter exponential family. Extensions for n independent random variables are given. A characterization for independent random variables involving order statistics is also given.

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.

Central Limit Theorems for Interchangeable Processes

1958 ◽  
Vol 10 ◽  
pp. 222-229 ◽  
Author(s):  
J. R. Blum ◽  
H. Chernoff ◽  
M. Rosenblatt ◽  
H. Teicher
Keyword(s):  
Stochastic Process ◽  
Probability Measure ◽  
Central Limit ◽  
Joint Distribution ◽  
Limit Theorems ◽  
Random Variables ◽  
Central Limit Theorems ◽  
Probability Measures ◽  
Image Position ◽  
Positive Integers

Let {Xn} (n = 1, 2 , …) be a stochastic process. The random variables comprising it or the process itself will be said to be interchangeable if, for any choice of distinct positive integers i 1, i 2, H 3 … , ik, the joint distribution of depends merely on k and is independent of the integers i 1, i 2, … , i k. It was shown by De Finetti (3) that the probability measure for any interchangeable process is a mixture of probability measures of processes each consisting of independent and identically distributed random variables.

scholarly journals Distribution of Minimal Path Lengths when Edge Lengths are Independent Heterogeneous Exponential Random Variables

2012 ◽  
Vol 49 (3) ◽  
pp. 895-900
Author(s):  
Sheldon M. Ross
Keyword(s):  
Joint Distribution ◽  
Shortest Paths ◽  
Random Variables ◽  
Simulated Data ◽  
Minimal Path ◽  
Exponential Random Variables ◽  
Path Lengths

We find the joint distribution of the lengths of the shortest paths from a specified node to all other nodes in a network in which the edge lengths are assumed to be independent heterogeneous exponential random variables. We also give an efficient way to simulate these lengths that requires only one generated exponential per node, as well as efficient procedures to use the simulated data to estimate quantities of the joint distribution.

Dependent Random Variables with Independent Subsets - II

1990 ◽  
Vol 33 (1) ◽  
pp. 24-28 ◽  
Author(s):  
Y. H. Wang
Keyword(s):  
Joint Distribution ◽  
Random Variables ◽  
Marginal Distributions ◽  
Dependent Random Variables ◽  
One Dimensional ◽  
The One

AbstractIn this paper, we consolidate into one two separate problems - dependent random variables with independent subsets and construction of a joint distribution with given marginals. Let N = {1,2,3,...} and X = {Xn; n ∊ N} be a sequence of random variables with nondegenerate one-dimensional marginal distributions {Fn; n ∊ N}. An example is constructed to show that there exists a sequence of random variables Y = {Yn; n ∊ N} such that the components of a subset of Y are independent if and only if its size is ≦ k, where k ≧ 2 is a prefixed integer. Furthermore, the one-dimensional marginal distributions of Y are those of X.

Representations and limit theorems for extreme value distributions

1978 ◽  
Vol 15 (03) ◽  
pp. 639-644 ◽  
Author(s):  
Peter Hall
Keyword(s):  
Stochastic Process ◽  
Order Statistics ◽  
Joint Distribution ◽  
Limit Theorems ◽  
Random Variables ◽  
Canonical Representation ◽  
Extreme Value ◽  
Limiting Distribution ◽  
Extreme Value Distributions ◽  
Independent Identically Distributed

LetXn1≦Xn2≦ ··· ≦Xnndenote the order statistics from a sample ofnindependent, identically distributed random variables, and suppose that the variablesXnn, Xn,n–1, ···, when suitably normalized, have a non-trivial limiting joint distributionξ1,ξ2, ···, asn → ∞. It is well known that the limiting distribution must be one of just three types. We provide a canonical representation of the stochastic process {ξn,n≧ 1} in terms of exponential variables, and use this representation to obtain limit theorems forξnasn →∞.

Sign in / Sign up

Export Citation Format

Share Document