Rayleigh mixture distribution

From Wikipedia, the free encyclopedia
Jump to: navigation, search

In probability theory and statistics a Rayleigh mixture distribution is a weighted mixture of multiple probability distributions where the weightings are equal to the weightings of a Rayleigh distribution.[1] Since the probability density function for a (standard) Rayleigh distribution is given by[2]

Rayleigh mixture distributions have probability density functions of the form

where is a well-defined probability density function or sampling distribution.[1]

The Rayleigh mixture distribution is one of many types of compound distributions in which the appearance of a value in a sample or population might be interpreted as a function of other underlying random variables. Mixture distributions are often used in mixture models, which are used to express probabilities of sub-populations within a larger population.

See also[edit]


  1. ^ a b Karim R., Hossain P., Begum S., and Hossain F., "Rayleigh Mixture Distribution", Journal of Applied Mathematics, Vol. 2011, doi:10.1155/2011/238290 (2011).
  2. ^ Jackson J.L., "Properties of the Rayleigh Distribution", Johns Hopkins University (1954).