f.Z.Weibull: Density function for the sum of two conditionally Weibull...

In mbannick/survDeconvolution: Survival Deconvolution

Description

If correlated, the function computes the density of Z by first marginalizing over the support of K, then over Y from 0 to z. For computational efficiency, it integrates K from epsilon to int.upper and Y from epsilon to z, where epsilon can be 0 and int.upper can be Inf. Small deviations from 0 and Inf will approximate the true integral.

Usage

f.Z.Weibull(z, parameters_x, parameters_y, gamma_shape, gamma_rate,
  epsilon, int.upper, control_list, correlated)

Arguments

z	A number or vector at which to evaluate the density function
parameters_x	A list, with an element named lambda (λ_x), and an element named p (p_x).
parameters_y	A list, with an element lambda (λ_y), and an element named p (p_y).
gamma_shape	A number, the shape parameter of Gamma frailty distribution
gamma_rate	A number, the rate parameter of Gamma frailty distribution
epsilon	A float, the lower bound for support of K and of Y
int.upper	A float, the upper bound for support of K
control_list	A list, with an element named rel.tol to be passed to distrExIntegrate as the rel.tol argument, and an element named subdivisions which is the maximum number of subintervals subdivisions argument in distrExIntegrate (see ?distrExIntegrate).
correlated	If FALSE, then X and Y are independent. If TRUE, then there is a shared frailty term K that induces correlation between X and Y.

Details

X \sim Weibull(shape=p_{x}, rate=λ_{x} \cdot k^{p_{x}})
Y \sim Weibull(shape=p_{y}, rate=λ_{y} \cdot k^{p_{y}})
Z := X + Y
K \sim Gamma(shape=gamma_shape, rate=gamma_rate)

Value

density function evaluated at Z=z.

mbannick/survDeconvolution documentation built on Sept. 30, 2020, 9:22 a.m.