Kumaraswamy distribution | Vose Software

# Kumaraswamy distribution

Format: Kumaraswamy(a, b)

The Kumaraswamy distribution is bounded at zero and 1 and can take a wide variety of shapes. It is therefore useful for many of the areas where the Beta distribution is used: the modeling of a prevalence, probability or fraction. Rescaling and shifting the distribution gives the Kumaraswamy4 distribution: a four-parameter bounded distribution like the Beta4 that can take on many shapes and any finite range. Examples of the Kumaraswamy distribution are given below:

## Uses

The Kumaraswamy distribution is sadly not yet widely used but, for example, it has been applied to model the storage volume of a reservoir (Fletcher and Ponnambalam, 1996) and system design. It has a simple form for its density and cumulative distributions, and is very flexible like the Beta distribution (which does not have simple forms for these functions). It will probably have a lot more applications as it becomes better known (tell your friends).

Poondi Kumaraswamy (1930 - 1988) was a leading Indian engineer and hydrologist. He introduced the distribution in Kumaraswamy (1980).

## ModelRisk functions added to Microsoft Excel for the Kumaraswamy distribution

VoseKumaraswamy generates random values from this distribution for Monte Carlo simulation, or calculates a percentile if used with a U parameter.

VoseKumaraswamyObject constructs a distribution object for this distribution.

VoseKumaraswamyProb returns the probability density or cumulative distribution function for this distribution.

VoseKumaraswamyProb10 returns the log10 of the probability density or cumulative distribution function.

VoseKumaraswamyFit generates values from this distribution fitted to data, or calculates a percentile from the fitted distribution.

VoseKumaraswamyFitObject constructs a distribution object of this distribution fitted to data.

VoseKumaraswamyFitP returns the parameters of this distribution fitted to data.