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In this paper, we derive the cumulative distribution functions (CDF) and probability density functions (PDF) of the ratio and product of two independent Weibull and Lindley random variables. The moment generating functions (MGF) and the k-moment are driven from the ratio and product cases. In these derivations, we use some special functions, for instance, generalized hypergeometric functions, confluent hypergeometric functions, and the parabolic cylinder functions. Finally, we draw the PDF and CDF in many values of the parameters. [ABSTRACT FROM AUTHOR]

We study matrix variate confluent hypergeometric function kind 1 distribution which is a generalization of the matrix variate gamma distribution. We give several properties of this distribution. We also derive density functions of X2-1/2X1X2-1/2, (X1+X2)-1/2X1(X1+X2)-1/2, and X1+X2, where m×m independent random matrices X1 and X2 follow confluent hypergeometric function kind 1 and gamma distributions, respectively. [ABSTRACT FROM AUTHOR]