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Research Article Open access CC BY 3.0

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/2014/10087

Abstract

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.

Characteristic function moment generating function GP3 distribution 3-parameter Weibull distribution.

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