Kurtosis of the Topp - Leone distributions

by Samuel Kotz and Edith Seier .

Abstract: When new probability distributions are defined, the insight we get about their characteristics can be of use to those wanting to use those distributions as models. In this note, the kurtosis of the Topp - Leone (T-L) family of distributions is explored by means of the spread-spread function. The T-L family with parameter b is compared , in terms of kurtosis, with the left triangular distribution that originated it. Based on the second derivative of the spread-spread function, three intervals of values of the parameter b are identified in which the kurtosis has a different behavior.

Key Words: Triangular distribution, Spread function, Spread-spread plots, Convexity

Samuel Kotz, kotz@gwu.edu
Edith Seier, seier@etsu.edu

Editor: N. Rao Chaganty, rchagant@odu.edu

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