coeffcomposite {distributionsrd} | R Documentation |
Determines the weights and cutoffs of the three-composite distribution numerically applying te continuity- and differentiability condition.
coeffcomposite(dist, coeff, startc = c(1, 1))
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). |
The continuity condition implies
α_1 = \frac{m_2(c_1) M_1(c_1)}{m_1(c_1)[M_2(c_2) - M_2(c_1)]}, \qquad α_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
Returns a named list containing a the separate distributions and their respective coefficients, as well as the cutoffs and weights of the composite distribution
# 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)) #'