distributionsrd (version 0.0.6)

coeffcomposite: Parametrise two-/three- composite distribution

Description

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

Usage

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).

Value

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

$$ \alpha_1 = \frac{m_2(c_1) M_1(c_1)}{m_1(c_1)[M_2(c_2) - M_2(c_1)]}, \qquad \alpha_2 = \frac{m_2(c_2) [1 - M_3(c_2)]}{m_3(c_2) [M_2(c_2) - M_2(c_1)]} $$

The differentiability condition implies

$$ \frac{d}{dc_1} ln[\frac{m_1(c_1)}{m_2(c_1)}] = 0, \qquad \frac{d}{dc_2} ln[\frac{m_2(c_2)}{m_3(c_2)}] = 0 $$

Examples

# NOT RUN {
# 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))
#'
# }