Search results
Results from the WOW.Com Content Network
If the points in the joint probability distribution of X and Y that receive positive probability tend to fall along a line of positive (or negative) slope, ρ XY is near +1 (or −1). If ρ XY equals +1 or −1, it can be shown that the points in the joint probability distribution that receive positive probability fall exactly along a straight ...
Suppose x is an n-dimensional random variable with joint density f. If y = G(x), where G is a bijective, differentiable function, then y has density p Y: = ...
In probability theory and statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional normal distribution to higher dimensions.
Every random vector gives rise to a probability measure on with the Borel algebra as the underlying sigma-algebra. This measure is also known as the joint probability distribution, the joint distribution, or the multivariate distribution of the random vector.
when joint probability density function between two random variables is known, the copula density function is known, and one of the two marginal functions are known, then, the other marginal function can be calculated, or
The probability distribution of the sum of two or more independent random variables is the convolution of their individual distributions. The term is motivated by the fact that the probability mass function or probability density function of a sum of independent random variables is the convolution of their corresponding probability mass functions or probability density functions respectively.
The original Vecchia method starts with the observation that the joint density of observations () = (, …,) can be written as a product of conditional distributions = = (, …,).
This rule allows one to express a joint probability in terms of only conditional probabilities. [4] The rule is notably used in the context of discrete stochastic processes and in applications, e.g. the study of Bayesian networks, which describe a probability distribution in terms of conditional probabilities.