A Fourier-analytic proof that conditional probability distributions exist on a group

1989 ◽  
pp. 1-5
Author(s):  
Michael S. Bingham
Keyword(s):  
Conditional Probability ◽  
Probability Distributions ◽  
Analytic Proof

scholarly journals Multiperiod conditional distribution functions for conditionally normal GARCH(1, 1) models

2005 ◽  
Vol 42 (02) ◽  
pp. 426-445
Author(s):  
Raymond Brummelhuis ◽  
Dominique Guégan
Keyword(s):  
Conditional Probability ◽  
Conditional Distribution ◽  
Probability Distributions ◽  
Random Variables ◽  
Distribution Functions ◽  
Tail Behavior ◽  
Asymptotic Tail

We study the asymptotic tail behavior of the conditional probability distributions of r t+k and r t+1+⋯+r t+k when (r t ) t∈ℕ is a GARCH(1, 1) process. As an application, we examine the relation between the extreme lower quantiles of these random variables.

Conditional Probability Distributions.

1975 ◽  
Vol 138 (4) ◽  
pp. 578
Author(s):  
J. F. C. Kingman ◽  
Tue Tjur
Keyword(s):  
Conditional Probability ◽  
Probability Distributions

Multivariate monotone likelihood ratio and uniform conditional stochastic order

1982 ◽  
Vol 19 (3) ◽  
pp. 695-701 ◽  
Author(s):  
Ward Whitt
Keyword(s):  
Conditional Probability ◽  
Likelihood Ratio ◽  
Probability Distributions ◽  
Stochastic Order ◽  
Total Positivity ◽  
Probability Measures ◽  
Monotone Likelihood Ratio ◽  
Fkg Inequality ◽  
The Fkg Inequality

Karlin and Rinott (1980) introduced and investigated concepts of multivariate total positivity (TP2) and multivariate monotone likelihood ratio (MLR) for probability measures on Rn These TP and MLR concepts are intimately related to supermodularity as discussed in Topkis (1968), (1978) and the FKG inequality of Fortuin, Kasteleyn and Ginibre (1971). This note points out connections between these concepts and uniform conditional stochastic order (ucso) as defined in Whitt (1980). ucso holds for two probability distributions if there is ordinary stochastic order for the corresponding conditional probability distributions obtained by conditioning on subsets from a specified class. The appropriate subsets to condition on for ucso appear to be the sublattices of Rn. Then MLR implies ucso, with the two orderings being equivalent when at least one of the probability measures is TP2.

On integrating the techniques of direct methods with anomalous dispersion: the one-phase structure seminvariants in the monoclinic and orthorhombic systems. II. Applications

1989 ◽  
Vol 45 (2) ◽  
pp. 163-165 ◽  
Author(s):  
D. Velmurugan ◽  
H. A. Hauptman ◽  
S. A. Potter
Keyword(s):  
Conditional Probability ◽  
Phase Structure ◽  
Probability Distributions ◽  
Direct Methods ◽  
Anomalous Dispersion ◽  
Test Results ◽  
Present Test ◽  
Free Data ◽  
The One

Applications are considered of the conditional probability distributions of the one-phase structure seminvariants in the monoclinic and orthorhombic systems when anomalous scatterers are present. Test results with error-free data show accurate estimates of seminvariants, the accuracy varying with the complexity of the structure and with the number and strength of the anomalous scatterers.

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