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