- Overview
- General Survival Distributions
- Exponential Distribution
- Weibull Distribution
- Gamma Distribution
- Lognormal Distribution
- Gompertz Distribution
- Log-logistic Distribution
- Generalized Gamma Distribution

This page summarizes common parametric distributions in R, based on the R functions shown in the table below.

Distribution | Density | CDF | Hazard | Cumulative hazard | Random sample |
---|---|---|---|---|---|

Exponential | dexp | pexp | flexsurv::hexp | flexsurv::Hexp | rexp |

Weibull (AFT) | dweibull | pweibull | flexsurv::hweibull | flexsurv::Hweibull | rweibull |

Gamma | dgamma | pgamma | flexsurv::hgamma | flexsurv::Hgamma | rgamma |

Lognormal | dlnorm | plnorm | flexsurv::hlnorm | flexsurv::Hlnorm | rlnorm |

Gompertz | flexsurv::dgompertz | flexsurv::pgompertz | flexsurv::hgompertz | flexsurv::Hgompertz | flexsurv::rgompertz |

Log-logistic | flexsurv::dllogis | flexsurv::pllogis | flexsurv::hllogis | flexsurv::Hllogis | flexsurv::rllogis |

Generalized gamma (Prentice 1975) | flexsurv::dgengamma | flexsurv::pgengamma | flexsurv::hgengamma | flexsurv::Hgengamma | flexsurv::rgengamma |

Survival function:

Hazard function:

Cumulative hazard function:

Median:

Notation: = rate

Density:

Survival:

Hazard:

Cumulative hazard:

Mean:

Median:

Regression:

Notation: = shape, = scale, = gamma function

Density:

Survival:

Hazard:

Cumulative hazard:

Mean:

Median:

Regression:

Notes: The exponential distribution is a special case of the Weibull with and

Notation: = shape, = rate, is the lower incomplete gamma function

Density:

Survival:

Mean:

Regression:

Notation: = mean, = variance, is the CDF of the standard normal distribution

Density:

Survival:

Mean:

Median:

Regression

Notation: = shape, = rate

Density:

Survival:

Hazard:

Cumulative Hazard:

Median:

Regression:

Notes: When the Gompertz distribution is equivalent to the exponential with constant hazard and rate .

Notation: = shape, = scale

Density:

Survival:

Hazard:

Median:

Mean: If , else undefined

Regression:

Notation: = location parameter, = scale parameter, = shape parameter

Density:

Regression:

Notes: Simplifies to lognormal when , Weibull when , exponential when , and gamma when