Generalized gamma distribution

Usage

dgeneralized_gamma(x, mu = 0, sigma = 1, Q, log = FALSE)

rgeneralized_gamma(n, mu = 0, sigma = 1, Q)

generalized_gamma(link = "log", link_sigma = "log", link_Q = "log")

Source

Bases on flexsurv (https://github.com/chjackson/flexsurv/tree/master) by Christopher Jackson chris.jackson@mrc-bsu.cam.ac.uk. Inspired by a blog post by Demetri Pananos (https://dpananos.github.io/posts/2023-12-02-gen-gamma/) and code by Krzysztof Sakrejda (https://github.com/sakrejda/tooling).

Arguments

x: Value, x > 0.
mu: Vector of “location” parameters.
sigma: Vector of scale'' parameters. Note the inconsistent meanings of the term scale” - this parameter is analogous to the (log-scale) standard deviation of the log-normal distribution, sdlog'' in [dlnorm()], rather than the scale” parameter of the gamma distribution dgamma(). Constrained to be positive.
Q: Vector of shape parameters.
log: logical; if TRUE the log-pdf is returned
n: number of observations.
link: Link function for mu
link_sigma: Link function for sigma
link_Q: Link function for Q

Value

dgeneralized_gamma gives the density, rgeneralized_gamma generates random deviates,

References

Prentice, R. L. (1974). A log gamma model and its maximum likelihood estimation. Biometrika 61(3):539-544.

Farewell, V. T. and Prentice, R. L. (1977). A study of distributional shape in life testing. Technometrics 19(1):69-75.

Lawless, J. F. (1980). Inference in the generalized gamma and log gamma distributions. Technometrics 22(3):409-419.

Cox, C., Chu, H., Schneider, M. F. and Muñoz, A. (2007). Parametric survival analysis and taxonomy of hazard functions for the generalized gamma distribution. Statistics in Medicine 26:4252-4374

Stacy, E. W. (1962). A generalization of the gamma distribution. Annals of Mathematical Statistics 33:1187-92