Characteristic and Moment Generating Functions of Generalised Pareto (GP3) and Weibull Distributions
G. Muraleedharan, C. Guedes Soares
Journal of Scientific Research and Reports · pp. 1861–1874 · Published 13 Jun 2014
10.9734/JSRR/2014/10087Abstract
The characteristic functions (CHFs) are derived for GP3 (generalized Pareto) distribution for shape parameters ξ ≠ 0 and ξ = 0 in explicit closed forms. The CHF of 3-parameter Weibull (type-3extreme value distribution (EVD)) is also derived in a closed form by a direct methodology. Moment-generating functions (MGFs) of the distributions are also derived and parametric relations of certain basic properties of the distributions are also obtained. Model estimation by the method of L-moments is also provided.
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