Group for Research in Decision Analysis

Strong competitors for beta and skew-normal distributions

Zohreh Javanshiri Ph.D. student, Ferdowsi University of Mashhad, Iran

Beta distribution is extremely versatile to model data restricted to any finite interval. This distribution has widespread applications in different areas. On the other hand, Kumaraswamy pleads that beta distribution does not fit hydrological data appropriately and proposed a new double bounded distribution named after him, we call Kw distribution, as an alternative to beta distribution.

Kw distribution has been used widely to analyze hydrology data. Several advantages of Kw distribution over the beta distribution are: the normalizing constant is very simple; simple explicit formulae for the distribution and quantile functions which do not involve any special functions; a simple formula for random variate generation; and explicit formulae for its moments and the moments of its order statistics. Generalized Kw distributions have been widely studied in statistics and numerous authors have developed various classes of these distributions. I suggest a generalization of Kw distribution, I call exp-Kumaraswamy (exp-Kw). The exp-Kw distribution, due to the flexibility of its hazard function could be an important model in a variety of problems in survival analysis. Also, a new distribution by transformation on exp-Kw distribution, as an alternative to skew-normal distribution, is obtained. The latter It has some advantages over skew-normal distribution. Its cdf, hrf and quantile function have closed form. Also, the ranges of skewness and kurtosis for this new distribution are wider than skew-normal distribution. So, the new distribution could be more appropriate for fitting skew and heavy tailed data. I end up the talk with fitting my developed distributions over real data.