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The K-distribution is a probability distribution that occurs as the result of a statistical or probabilistic model used in Synthetic Aperture Radar (SAR) imagery. The K distribution is created by compounding two different probability distributions, where one representing the radar cross-section and the other one representing speckle that is a feature of coherent imaging.
This model is used to present the observed intensity X, includes compounding two gamma distributions. In all cases a reparameterisation of the common form of the family of gamma distributions is used, such that the parameters are as follows:
• the usual shape parameter and
• the mean of the distribution
The model is such that X has a gamma distribution with mean σ and shape parameter L, with σ treated as a random variable and having another gamma distribution, this time with mean μ and shape parameter ν. The outcome is that X has the following density function (x > 0):

here K is a modified Bessel function of the second kind. In this complete derivation, the K-distribution is a compound probability distribution and also a product distribution. Product distribution is the distribution of the product of two independent random variables, one having a gamma distribution with mean μ and shape parameter ν and the second having a gamma distribution with mean 1 and shape parameter L.
Jakeman and Pusey in 1978 derive this distribution on paper.
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