frailty_laplace: Laplace Transform and Derivatives for Frailty Distributions

In MultiFrailty: Shared Frailty Regression Models with Inverse Gaussian, Generalized Lindley, and Gamma Frailty Distributions

Laplace Transform and Derivatives for Frailty Distributions

Description

Computes Laplace transform L(s), first derivative L'(s), and frailty variance Var(W) for five frailty families: "none", "gamma", "ig", "gl1", and "gl2".

Usage

frailty_laplace(
  s,
  frailty = c("none", "gamma", "ig", "gl1", "gl2"),
  par = numeric(0)
)

Arguments

s	Non-negative numeric vector.
frailty	Character string specifying frailty family: "none", "gamma", "ig", "gl1", or "gl2".
par	Numeric vector of parameters per family: numeric(0) for "none", c(theta) for "gamma", c(eta) for "ig", c(eta, epsilon) for "gl1", or c(theta, mu) for "gl2".

Value

A named list with components:

L	Laplace transform L(s).
L1	First derivative L'(s).
Var	Variance of frailty distribution Var(W), evaluated as L”(0) - 1.

References

Hougaard, P. (1984). Life table methods for heterogeneous populations: distributions of frailties. Biometrika, 71(1), 75-83.

Pandey, A., Hanagal, D. D., & Tyagi, S. (2022). Shared Frailty Models Based on Cancer Data. International Journal of Statistics and Reliability Engineering, 9(3), 461-474.

Pandey, A., & Tyagi, S. (2021). Comparison of Multiplicative Frailty Models Under Weibull Baseline Distribution. Lobachevskii Journal of Mathematics, 42(13), 3184-3195.

Examples

fl_gamma <- frailty_laplace(s = 0.5, frailty = "gamma", par = c(0.8))
fl_gl1   <- frailty_laplace(s = 0.5, frailty = "gl1", par = c(1.2, 0.5))
fl_gl2   <- frailty_laplace(s = 0.5, frailty = "gl2", par = c(1.5, 0.8))

MultiFrailty documentation built on Aug. 8, 2026, 1:07 a.m.