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In probability theory and statistics, the multivariate normal distribution, ... then the distribution of x 1 conditional on x 2 = a is multivariate normal ...
The multinomial distribution, a generalization of the binomial distribution. The multivariate normal distribution, a generalization of the normal distribution. The multivariate t-distribution, a generalization of the Student's t-distribution. The negative multinomial distribution, a generalization of the negative binomial distribution.
If the conditional distribution of given is a continuous distribution, then its probability density function is known as the conditional density function. [1] The properties of a conditional distribution, such as the moments , are often referred to by corresponding names such as the conditional mean and conditional variance .
One common method of construction of a multivariate t-distribution, for the case of dimensions, is based on the observation that if and are independent and distributed as (,) and (i.e. multivariate normal and chi-squared distributions) respectively, the matrix is a p × p matrix, and is a constant vector then the random variable = / / + has the density [1]
There is a set of probability distributions used in multivariate analyses that play a similar role to the corresponding set of distributions that are used in univariate analysis when the normal distribution is appropriate to a dataset. These multivariate distributions are: Multivariate normal distribution; Wishart distribution
In probability theory, the conditional expectation, conditional expected value, or conditional mean of a random variable is its expected value evaluated with respect to the conditional probability distribution. If the random variable can take on only a finite number of values, the "conditions" are that the variable can only take on a subset of ...
where () = [= ()] and = is the Fisher information of Y relative to calculated with respect to the conditional density of Y given a specific value X = x. As a special case, if the two random variables are independent , the information yielded by the two random variables is the sum of the information from each random variable separately:
In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed.Thus, if the random variable X is log-normally distributed, then Y = ln(X) has a normal distribution.