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In the paper the basic analytical properties of the MacDonald function (the modified Bessel function of the second kind) are summarized and the properties of some subclasses of distribution functions based on MacDonald function, especially of the types $x^n{K}_n\left(x\right),x\ge 0,{\left|x\right|}^n{K}_n\left(x\left|x\right|\right),x\in 𝐑$ and $x^{n+1}{K}_n\left(x\right),x\ge 0$ are discussed. The distribution functions mentioned are useful for analytical modelling of composed (mixed) distributions, especially for products of random variables having distributions of the exponential type. Extensive and useful applications...