Characteristic and Moment Generating Functions of Generalised Pareto (GP3) and Weibull Distributions
G. Muraleedharan *
Centre for Marine Technology and Engineering (CENTEC), Instituto Superior Técnico, Technical University of Lisbon, Av.Rovisco Pais, 1049-001, Lisboa, Portugal.
C. Guedes Soares
Centre for Marine Technology and Engineering (CENTEC), Instituto Superior Técnico, Technical University of Lisbon, Av.Rovisco Pais, 1049-001, Lisboa, Portugal.
*Author to whom correspondence should be addressed.
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.
Keywords: Characteristic function, moment generating function, GP3 distribution, 3-parameter Weibull distribution.