coeffcomposite function

Parametrise two-/three- composite distribution

Parametrise two-/three- composite distribution

Determines the weights and cutoffs of the three-composite distribution numerically applying te continuity- and differentiability condition.

coeffcomposite(dist, coeff, startc = c(1, 1))

Arguments

  • dist: character vector denoting the distribution of the first-, second- (and third) component respectively. If only two components are provided, the distribution reduces to the two-component distribution.
  • coeff: named numeric vector holding the coefficients of the first-, second- (and third) component, predeced by coeff1., coeff2. (and coeff3.), respectively. Coefficients for the last component do not have to be provided for the two-component distribution and will be disregarded.
  • startc: starting values for the lower and upper cutoff, defaults to c(1,1).

Returns

Returns a named list containing a the separate distributions and their respective coefficients, as well as the cutoffs and weights of the composite distribution

Details

The continuity condition implies

α1=m2(c1)M1(c1)m1(c1)[M2(c2)−M2(c1)],α2=m2(c2)[1−M3(c2)]m3(c2)[M2(c2)−M2(c1)] \alpha_1 = \frac{m_2(c_1) M_1(c_1)}{m_1(c_1)[M_2(c_2) - M_2(c_1)]}, \qquad \alpha_2 = \frac{m_2(c_2) [1 - M_3(c_2)]}{m_3(c_2) [M_2(c_2) - M_2(c_1)]}

The differentiability condition implies

ddc1ln[m1(c1)m2(c1)]=0,ddc2ln[m2(c2)m3(c2)]=0 \frac{d}{dc_1} ln[\frac{m_1(c_1)}{m_2(c_1)}] = 0, \qquad \frac{d}{dc_2} ln[\frac{m_2(c_2)}{m_3(c_2)}] = 0

Examples

# Three-composite distribution
dist <- c("invpareto", "lnorm", "pareto")
coeff <- c(coeff1.k = 1, coeff2.meanlog = -0.5, coeff2.sdlog = 0.5, coeff3.k = 1)
coeffcomposite(dist = dist, coeff = coeff, startc = c(1, 1))

# Two-composite distribution
dist <- c("lnorm", "pareto")
coeff <- c(coeff1.meanlog = -0.5, coeff1.sdlog = 0.5, coeff2.k = 1.5)
coeffcomposite(dist = dist, coeff = coeff, startc = c(1, 1))

dist <- c("invpareto", "lnorm")
coeff <- c(coeff1.k = 1.5, coeff2.meanlog = 2, coeff2.sdlog = 0.5)
coeffcomposite(dist = dist, coeff = coeff, startc = c(1, 1))
#'
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  • Maintainer: Ruben Dewitte
  • License: GPL-3
  • Last published: 2020-05-25

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