Kumaraswamy distribution

In probability and statistics, the Kumaraswamy's double bounded distribution is a family of continuous probability distributions defined on the interval (0,1). It is similar to the Beta distribution, but much simpler to use especially in simulation studies since its probability density function, cumulative distribution function and quantile functions can expressed in closed form. This distribution was originally proposed by Poondi Kumaraswamy for variables that are lower and upper bounded. In probability and statistics, the Kumaraswamy's double bounded distribution is a family of continuous probability distributions defined on the interval (0,1). It is similar to the Beta distribution, but much simpler to use especially in simulation studies since its probability density function, cumulative distribution function and quantile functions can expressed in closed form. This distribution was originally proposed by Poondi Kumaraswamy for variables that are lower and upper bounded. The probability density function of the Kumaraswamy distribution is and where a and b are non-negative shape parameters. The cumulative distribution function is In its simplest form, the distribution has a support of (0,1). In a more general form, the normalized variable x is replaced with the unshifted and unscaled variable z where: The raw moments of the Kumaraswamy distribution are given by: where B is the Beta function and Γ(.) denotes the Gamma function. The variance, skewness, and excess kurtosis can be calculated from these raw moments. For example, the variance is: The Shannon entropy (in nats) of the distribution is: where H i {displaystyle H_{i}} is the harmonic number function.