Procrustean Strategies for Incompatible Conditional and Marginal Information

2005 ◽  
Vol 56 (1-4) ◽  
pp. 17-34
Author(s):  
Barry C. Arnold
Keyword(s):  
Joint Distribution ◽  
Partial Information ◽  
Bivariate Distribution

Summary Full or partial information about the marginals and conditionals of a bivariate distribution is likely to be incompatible. Additionally, information may come from heterogenous sources with limited agreement between sources. Some strategies for selecting a single “minimally incompatible” joint distribution are surveyed.

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.

A bivariate distribution in regeneration

1975 ◽  
Vol 12 (4) ◽  
pp. 837-839 ◽  
Author(s):  
Kai Lai Chung
Keyword(s):  
Boundary Point ◽  
Joint Distribution ◽  
Bivariate Distribution ◽  
Regenerative Phenomenon

The joint distribution of the time since last exit, and the time until next entrance, into a unique boundary point is given in Formula (1) below. The boundary point may be replaced by a regenerative phenomenon.

scholarly journals Tuning the Bivariate Meta-Gaussian Distribution Conditionally in Quantifying Precipitation Prediction Uncertainty

Forecasting ◽  
2020 ◽  
Vol 2 (1) ◽  
pp. 1-19 ◽  
Author(s):  
Limin Wu
Keyword(s):  
Gaussian Distribution ◽  
Conditional Distribution ◽  
Joint Distribution ◽  
Goodness Of Fit ◽  
Pearson Correlation ◽  
Parameter Tuning ◽  
Bivariate Distribution ◽  
Distribution Model ◽  
Standard Normal ◽  
Forecast Variable

One of the ways to quantify uncertainty of deterministic forecasts is to construct a joint distribution between the forecast variable and the observed variable; then, the uncertainty of the forecast can be represented by the conditional distribution of the observed given the forecast. The joint distribution of two continuous hydrometeorological variables can often be modeled by the bivariate meta-Gaussian distribution (BMGD). The BMGD can be obtained by transforming each of the two variables to a standard normal variable and the dependence between the transformed variables is provided by the Pearson correlation coefficient of these two variables. The BMGD modeling is exact provided that the transformed joint distribution is standard normal. In real-world applications, however, this normality assumption is hardly fulfilled. This is often the case for the modeling problem we consider in this paper: establish the joint distribution of a forecast variable and its corresponding observed variable for precipitation amounts accumulated over a duration of 24 h. In this case, the BMGD can only serve as an approximate model and the dependence parameter can be estimated in a variety of ways. In this paper, the effect of tuning this parameter is studied. Numerical simulations conducted suggest that, while the parameter tuning results in limited improvements in goodness-of-fit (GOF) for the BMGD as a bivariate distribution model, better results may be achieved by tuning the parameter for the one-dimensional conditional distribution of the observed given the forecast greater than a certain large value.

Mass transportation problems with capacity constraints

1999 ◽  
Vol 36 (2) ◽  
pp. 433-445 ◽  
Author(s):  
S. T. Rachev ◽  
I. Olkin
Keyword(s):  
Joint Distribution ◽  
Bivariate Distribution ◽  
Capacity Constraints ◽  
Distribution Functions ◽  
Mass Transportation ◽  
Marginal Distributions ◽  
Transportation Problems ◽  
The Family ◽  
Additional Capacity ◽  
Additional Constraints

We exhibit solutions of Monge–Kantorovich mass transportation problems with constraints on the support of the feasible transportation plans and additional capacity restrictions. The Hoeffding–Fréchet inequalities are extended for bivariate distribution functions having fixed marginal distributions and satisfying additional constraints. Sharp bounds for different probabilistic functionals (e.g. Lp-distances, covariances, etc.) are given when the family of joint distribution functions has prescribed marginal distributions, satisfies restrictions on the support, and is bounded from above, or below, by other distributions.

scholarly journals Measures for concordance and discordance with applications in disease control and prevention

2018 ◽  
Vol 28 (10-11) ◽  
pp. 3086-3099 ◽  
Author(s):  
Marc Aerts ◽  
Adelino JC Juga ◽  
Niel Hens
Keyword(s):  
Odds Ratio ◽  
Joint Distribution ◽  
Bivariate Distribution ◽  
Alternative Measure ◽  
Index Test ◽  
Response Data ◽  
Control And Prevention ◽  
Depression Disorders ◽  
Joint Characteristic ◽  
Synchrony Measure

Bivariate binary response data appear in many applications. Interest goes most often to a parameterization of the joint probabilities in terms of the marginal success probabilities in combination with a measure for association, most often being the odds ratio. Using, for example, the bivariate Dale model, these parameters can be modelled as function of covariates. But the odds ratio and other measures for association are not always measuring the (joint) characteristic of interest. Agreement, concordance, and synchrony are in general facets of the joint distribution distinct from association, and the odds ratio as in the bivariate Dale model can be replaced by such an alternative measure. Here, we focus on the so-called conditional synchrony measure. But, as indicated by several authors, such a switch of parameter might lead to a parameterization that does not always lead to a permissible joint bivariate distribution. In this contribution, we propose a new parameterization in which the marginal success probabilities are replaced by other conditional probabilities as well. The new parameters, one homogeneity parameter and two synchrony/discordance parameters, guarantee that the joint distribution is always permissible. Moreover, having a very natural interpretation, they are of interest on their own. The applicability and interpretation of the new parameterization is shown for three interesting settings: quantifying HIV serodiscordance among couples in Mozambique, concordance in the infection status of two related viruses, and the diagnostic performance of an index test in the field of major depression disorders.

MODELS BASED ON PARTIAL INFORMATION ABOUT SURVIVAL AND HAZARD GRADIENT

2010 ◽  
Vol 24 (4) ◽  
pp. 561-584 ◽  
Author(s):  
Majid Asadi ◽  
Somayeh Ashrafi ◽  
Nader Ebrahimi ◽  
Ehsan S. Soofi
Keyword(s):  
Joint Distribution ◽  
Partial Information ◽  
Survival Function ◽  
Information Criteria ◽  
Hazard Rates ◽  
Optimal Model ◽  
Dynamic Information ◽  
Hazard Gradient ◽  
Other Information ◽  
Gumbel Model

This article develops information optimal models for the joint distribution based on partial information about the survival function or hazard gradient in terms of inequalities. In the class of all distributions that satisfy the partial information, the optimal model is characterized by well-known information criteria. General results relate these information criteria with the upper orthant and the hazard gradient orderings. Applications include information characterizations of the bivariate Farlie–Gumbel–Morgenstern, bivariate Gumbel, and bivariate generalized Gumbel, for which no other information characterization are available. The generalized bivariate Gumbel model is obtained from partial information about the survival function and hazard gradient in terms of marginal hazard rates. Other examples include dynamic information characterizations of the bivariate Lomax and generalized bivariate Gumbel models having marginals that are transformations of exponential such as Pareto, Weibull, and extreme value. Mixtures of bivariate Gumbel and generalized Gumbel are obtained from partial information given in terms of mixtures of the marginal hazard rates.

Mass transportation problems with capacity constraints

1999 ◽  
Vol 36 (02) ◽  
pp. 433-445 ◽  
Author(s):  
S. T. Rachev ◽  
I. Olkin
Keyword(s):  
Joint Distribution ◽  
Bivariate Distribution ◽  
Capacity Constraints ◽  
Distribution Functions ◽  
Mass Transportation ◽  
Marginal Distributions ◽  
Transportation Problems ◽  
The Family ◽  
Additional Capacity ◽  
Additional Constraints

We exhibit solutions of Monge–Kantorovich mass transportation problems with constraints on the support of the feasible transportation plans and additional capacity restrictions. The Hoeffding–Fréchet inequalities are extended for bivariate distribution functions having fixed marginal distributions and satisfying additional constraints. Sharp bounds for different probabilistic functionals (e.g.Lp-distances, covariances, etc.) are given when the family of joint distribution functions has prescribed marginal distributions, satisfies restrictions on the support, and is bounded from above, or below, by other distributions.

scholarly journals Reliability for some bivariate gamma distributions

2005 ◽  
Vol 2005 (2) ◽  
pp. 151-163 ◽  
Author(s):  
Saralees Nadarajah
Keyword(s):  
Joint Distribution ◽  
Special Functions ◽  
Random Variables ◽  
Bivariate Distribution ◽  
Independent Random Variables ◽  
Algebraic Form ◽  
Gamma Distributions ◽  
Strength Models ◽  
Explicit Expressions

In the area of stress-strength models, there has been a large amount of work as regards estimation of the reliabilityR=Pr(X<Y). The algebraic form forR=Pr(X<Y)has been worked out for the vast majority of the well-known distributions whenXandYare independent random variables belonging to the same univariate family. In this paper, we consider forms ofRwhen(X,Y)follows a bivariate distribution with dependence betweenXandY. In particular, we derive explicit expressions forRwhen the joint distribution is bivariate gamma. The calculations involve the use of special functions.

scholarly journals Reliability for some bivariate beta distributions

2005 ◽  
Vol 2005 (1) ◽  
pp. 101-111 ◽  
Author(s):  
Saralees Nadarajah
Keyword(s):  
Joint Distribution ◽  
Special Functions ◽  
Random Variables ◽  
Bivariate Distribution ◽  
Independent Random Variables ◽  
Algebraic Form ◽  
Beta Distributions ◽  
Strength Models ◽  
Explicit Expressions

In the area of stress-strength models there has been a large amount of work as regards estimation of the reliabilityR=Pr(X<Y). The algebraic form forR=Pr(X<Y)has been worked out for the vast majority of the well-known distributions whenXandYare independent random variables belonging to the same univariate family. In this paper, we consider forms ofRwhen(X,Y)follows a bivariate distribution with dependence betweenXandY. In particular, we derive explicit expressions forRwhen the joint distribution is bivariate beta. The calculations involve the use of special functions.

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