ecd.cusp_std_moment: The moments, characteristic function (CF), and moment...

In ecd: Elliptic Lambda Distribution and Option Pricing Model

The moments, characteristic function (CF), and moment generating function (MGF) of standard cusp distribution.

Description

The moments of standard cusp distribution are calculated via Gamma function. The CF and MGF are calculated as sum of moment terms. The CF is a complex number. Since the terms in MGF is ultimately diverging, the sum is truncated before the terms are increasing.

Usage

ecd.cusp_std_moment(n)

ecd.cusp_std_cf(t, mu = 0, sigma = 1, rel.tol = 1e-08, show.warning = FALSE)

ecd.cusp_std_mgf(t, mu = 0, sigma = 1, rel.tol = 1e-07, show.warning = FALSE)

Arguments

n	integer vector specifying the n-th moments
t	numeric vector for CF and MGF
mu	length-one numeric, specifying mean for CF and MGF
sigma	length-one numeric, specifying volatility for CF and MGF
rel.tol	relative tolerance
show.warning	logical, to show warning or not.

Value

the values of the moments, CF, MGF

Examples

ecd.cusp_std_moment(c(2,4))

ecd documentation built on May 10, 2022, 1:07 a.m.