ii) Kumaraswamy Distribution In this distribution, the probability density function of a random variable X is given by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7) with the cumulative density function (or distribution function), given as [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8) In probability theory Kumaraswamy's double bounded distribution is as versatile as the beta distribution, but much simpler to use especially in simulation studies as it has a simple closed form for both the p.

R] (x) are the probability density function and the cumulative density function of the random sectional resistance, R, and, similarly, [f.