# conditional distribution

## conditional distribution

[kən′dish·ən·əl dis·trə′byü·shən]
(statistics)
If W and Z are random variables with discrete values w1, w2,…, and z1, z2,…, the conditional distribution of W given Z = z is the distribution which assigns to wi, i = 1,2,…, the conditional probability of W = wi given Z = z.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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Second, Equation (3) can be used recursively to obtain the conditional distribution at longer horizons:
Using the conditional mean and the conditional variance obtained from the estimated GARCH family models, the quantiles of the conditional distribution can be easily obtained for the calculation of VaR (Tsay, 2005).
If Yt, t = 1,2,...,T, follows a gamma conditional distribution G([p.sub.t], [q.sub.t] ), where G(p,q) denotes a gamma distribution with mean pq and variance [pq.sup,2], the conditional mean and variance are related to the original parameters by the equations [[micro].sub.t]= p.sub.t [q.sub.t] and [h.sub.t = [[micro].sub.t] [q.sub.t].
Secondly, quantile regressions are performed in order to observe whether there are any heterogeneous effects along the conditional distribution of the two measures of export activity.
This is very important to our estimation of the conditional distribution function and its inverse.
Lemahieu, "Source extraction by maximizing the variance in the conditional distribution tails," IEEE Transactions on Signal Processing, vol.
For a binary variable, a Bernoulli-Bernoulli energy function [34, 35] and the conditional distribution of a single stochastic hidden variable are given by
where [r.sub.t] stands for risk-free interest rate; [[epsilon].sub.t] satisfies certain conditional distribution process, that is, [[epsilon].sub.t] | [[phi].sub.t] ~ D(0, [h.sub.t]), where [h.sub.t] stands for conditional variance satisfying [h.sub.t] = P([h.sub.t-1], [[epsilon].sub.t-1]).
What this means is that the conditional distribution of [X.sub.t] given observations of the process at several moments in the past, is the same as the one given only the latest observation.
By capturing the full conditional distribution rather than a single estimate, the method can directly characterize the uncertainty in model predictions.
By applying the conditional distribution theorem, the joint PDF discussed in (4) can be described as
However, (5) does not consider the role of each feature on reducing the mismatch of conditional distribution. Therefore, it is natural to select the features that can reduce the mismatch of conditional distribution.

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