success (version 1.0.1)

exp_hazards: Exponential hazard, cumulative hazard and inverse cumulative hazard

Description

Functions which return the hazard, cumulative hazard and inverse cumulative hazard at time t for an exponential distribution with parameter $\lambda$ and true hazard ratio $\mu$.

Usage

haz_exp(t, lambda, mu = log(1))
chaz_exp(t, lambda, mu = log(1))
inv_chaz_exp(t, lambda, mu = log(1))

Value

Value of specified function at time $t$.

Arguments

t

time of evaluation.

lambda

parameter of the exponential distribution.

mu

(optional) true excess hazard rate $\mu$.

Details

The hazard function of an exponential distribution is given by: $$h(t|\lambda ,\mu )=\lambda e^{\mu }$$ The cumulative hazard (with true hazard ratio $\mu$) is given by: $$H(t|\lambda ,\mu )=\lambda t{e}^{\mu }$$ The inverse cumulative hazard (with true hazard ratio $\mu$) by: $$H^{-1}(t|\lambda ,\mu )=\frac{t}{\lambda e^{\mu }}$$