weib_hazards: Weibull hazard, cumulative hazard and inverse cumulative...

In success: Survival Control Charts Estimation Software

Weibull hazard, cumulative hazard and inverse cumulative hazard

Description

Functions which return the hazard, cumulative hazard and inverse cumulative hazard at time t for a Weibull distribution with shape parameter \lambda, scale parameter \theta and true hazard ratio \mu.

Usage

haz_weib(t, lambda, theta, mu = log(1))

chaz_weib(t, lambda, theta, mu = log(1))

inv_chaz_weib(t, lambda, theta, mu = log(1))

Arguments

t	time of evaluation.
lambda	shape parameter \lambda
theta	scale parameter \theta
mu	(optional) true excess hazard rate \mu.

Details

The hazard function of a Weibull distribution is given by:

h(t| \lambda, \theta, \mu) = \frac{\lambda}{\theta} \left(\frac{t}{\theta} \right)^{\lambda -1} e^\mu

The cumulative hazard (with true hazard ratio \mu) is given by:

H(t| \lambda, \theta, \mu) = \left( \frac{t}{\theta} \right)^{\lambda} e^\mu

The inverse cumulative hazard (with true hazard ratio \mu) by:

H^{-1}(t| \lambda, \theta, \mu) = \theta \left( \frac{t}{e^\mu} \right)^{1/\lambda}

Value

Value of specified function at time t.

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