A SKEWED TRUNCATED PEARSON TYPE Ⅶ DISTRIBUTION

摘要

Skewed symmetric distributions have attracted a great deal of attention in the last few years. One of them, the skewed Pearson type Ⅶ distribution suffers from limited applicability because it is well known that the Pearson type Ⅶ distribution does not have finite moments of all orders. This note proposes an alternative referred to as skewed truncated Pearson type Ⅶ distribution and defined by the pdf f(x), = 2g(x)G(λx), where g(·) and G(·) are taken, respectively, to be the pdf and the cdf of a truncated Pearson type Ⅶ distribution. This distribution possesses finite moments of all orders and could therefore be a better model for certain practical situations. Two such situations are discussed. The note also derives various properties of the distribution, including its moments.