f.YZ.Weibull: Joint density function for two conditionally Weibull random...

In mbannick/survDeconvolution: Survival Deconvolution

Description

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

Usage

f.YZ.Weibull(y, z, parameters_x, parameters_y, gamma_shape, gamma_rate,
  epsilon, control_list, int.upper, correlated = TRUE)

Arguments

y	A number at which to evaluate the density Y = y
z	A number at which to evaluate the density X = z-y
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
control_list	A list, with an element named rel.tol to be passed to 'distrExIntegrate' as the rel.tol argument (see ?distrExIntegrate)
int.upper	A float, the upper bound for support of K
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 \to X = Z - Y
K \sim Gamma(shape=gamma_shape, rate=gamma_rate)

Value

joint density function evaluated at Y=y, and X=z-y.

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