Density, distribution function, quantile function and random generation for a generalisation of the exponential distribution, in which the rate changes at a series of times.
1 2 3 4 
x,q 
vector of quantiles. 
p 
vector of probabilities. 
n 
number of observations. If 
rate 
vector of rates. 
t 
vector of the same length as 
log, log.p 
logical; if TRUE, probabilities p are given as log(p), or log density is returned. 
lower.tail 
logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]. 
Consider the exponential distribution with rates r1,…, rn changing at times t1, …, tn, with t1 = 0. Suppose tk is the maximum ti such that ti < x. The density of this distribution at x > 0 is f(x) for k = 1, and
∏{i=1 … k} (1  F(ti  t{i1}, r{i1})) f(x  tk, rk)
for k > 1.
where F() and f() are the distribution and density functions of the standard exponential distribution.
If rate
is of length 1, this is just the standard exponential
distribution. Therefore, for example, dpexp(x)
, with no other
arguments, is simply equivalent to dexp(x)
.
Only rpexp
is used in the msm
package, to simulate
from Markov processes with piecewiseconstant intensities depending on
timedependent covariates. These functions are merely provided for
completion, and are not optimized for numerical stability or speed.
dpexp
gives the density, ppexp
gives the distribution
function, qpexp
gives the quantile function, and rpexp
generates random deviates.
C. H. Jackson chris.jackson@mrcbsu.cam.ac.uk
1 2 3 4 5 6 7 8 9 10 11  x < seq(0.1, 50, by=0.1)
rate < c(0.1, 0.2, 0.05, 0.3)
t < c(0, 10, 20, 30)
## standard exponential distribution
plot(x, dexp(x, 0.1), type="l")
## distribution with piecewise constant rate
lines(x, dpexp(x, rate, t), type="l", lty=2)
## standard exponential distribution
plot(x, pexp(x, 0.1), type="l")
## distribution with piecewise constant rate
lines(x, ppexp(x, rate, t), type="l", lty=2)

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