Appendix A.3: Probability Distributions: Distributional mixtures
[this page | pdf | back links]
A random variable is distributed according to a normal mixture distribution if it is of the form where and are independent random variables, is a non-negative random variable, and is some function of . For example, the t distribution has and being chi-squared with degrees of freedom and the standard non-central t distribution has where is the non-centrality parameter and is chi-squared with degrees of freedom.
A distributional mixture of normal distributions is to be interpreted more generally as any distribution in which the overall random variable is selected with probability from a (typically finite) number of normal random distributions, the ’th one of which is for arbitrary constant and . Any univariate distribution can be approximated arbitrarily accurately with a large enough number of underlying normal random distributions. It is contrasted with a linear combination mixture of normal distributions in which the overall random variable is derived by adding together a linear combination of underlying normal random variables, i.e. .
NAVIGATION LINKSContents | Prev | Next