exp_hazards: Exponential hazard, cumulative hazard and inverse cumulative...

In success: Survival Control Charts Estimation Software

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))

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}

Value

Value of specified function at time t.

success documentation built on June 22, 2024, 10:19 a.m.