In a finite mixture model the distribution of the random variable X has a known form (e.g. normal), but the values of the parameters of the distribution are not known. Instead, it is known that the vector of the parameters takes one of the values θ1, θ2,…, θm with associated probabilities w1, w2,…, wm. If, for a continuous random variable, the probability density function of the kth of the possible distributions is denoted by f(x, θk), then the finite mixture distribution of X is given by . An equivalent result holds for a discrete random variable.
Subjects: Probability and Statistics.