Journal
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
Volume 42, Issue 5, Pages 741-755Publisher
TAYLOR & FRANCIS INC
DOI: 10.1080/03610926.2011.581782
Keywords
Beta distribution; Closeness properties; Dispersion bounds; Kumaraswamy distribution; Limiting distributions; Mean absolute deviation around the median; Moments; Primary 60E05; Secondary 62E99
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The Kumaraswamy distribution is very similar to the Beta distribution but has the key advantage of a closed-form cumulative distribution function. This makes it much better suited than the Beta distribution for computation-intensive activities like simulation modeling and the estimation of models by simulation-based methods. However, in spite of the fact that the Kumaraswamy distribution was introduced in 1980, further theoretical research on the distribution was not developed until very recently (Garg, 2008; Jones, 2009; Mitnik, 2009; Nadarajah, 2008). This article contributes to this recent research and: (a) shows that Kumaraswamy variables exhibit closeness under exponentiation and under linear transformation; (b) derives an expression for the moments of the general form of the distribution; (c) specifies some of the distribution's limiting distributions; and (d) introduces an analytical expression for the mean absolute deviation around the median as a function of the parameters of the distribution, and establishes some bounds for this dispersion measure and for the variance.
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