conditional piecewise exponential {PWEXP}

The Conditional Piecewise Exponential Distribution

Description

Distribution function, quantile function and random generation for the piecewise exponential distribution t with piecewise rate rate given t>qT.

Usage

ppwexp_conditional(q, qT, rate=1, breakpoint=NULL, lower.tail=TRUE,
                   log.p=FALSE, one_piece, safety_check=TRUE)
qpwexp_conditional(p, qT, rate=1, breakpoint=NULL, lower.tail=TRUE,
                   log.p=FALSE, one_piece, safety_check=TRUE)
rpwexp_conditional(n, qT, rate, breakpoint=NULL)

Arguments

q

vector of quantiles.

p

vector of probabilities.

qT

the distribution is conditional on t>qT. qT can be a scalar or a vector with the same length of q or p.

n

number of observations. Must be a positive integer with length 1.

rate

a vector of rates in each piece.

breakpoint

a vector of breakpoints. The length is length(rate)-1. Can be NULL if rate is a single value.

log, log.p

logical; if TRUE, probabilities p are given as log(p).

lower.tail

logical; if TRUE (default), probabilities are P[X \le x], otherwise, P[X > x].

one_piece

(only required when safety_check=FALSE) whether the distribution only has one piece (i.e., rate is a single value and breakpoint=NULL).

safety_check

logical; whether check the input arguments; if FALSE, function has better computing performance by skipping all safety checks.

Details

See webpage https://zjph602xtc.github.io/PWEXP/ for more details for its survival function, cumulative density function, quantile function.

Value

ppwexp_conditional gives the conditional distribution function, qpwexp_conditional gives the conditional quantile function, and rpwexp_conditional generates conditional random variables.

The length of the result is determined by q, p or n for ppwexp_conditional, qpwexp_conditional or rpwexp_conditional. You can only specify a single piecewise exponential distribution every time you call these functions. This is different from the exponential distribution functions in package stats.

When the length of qT is 1, then all results are conditional on the same t>qT. In rpwexp_conditional, qT must be a scalar. When the length of qT equals to the length of q or p, then each value in the result is conditional on t>qT for each value in qT.

Arguments rate and breakpoint must match. The length of rate is the length of breakpoint + 1.

Author(s)

Tianchen Xu [e-mail]

See Also

dpwexp, ppwexp, qpwexp, rpwexp

Examples

# CDF and qunatile function of conditional piecewise exp with rate 2, 1, 3 given t > 0.1
t <- seq(0.1, 1.2, 0.01)
F2_con <- ppwexp_conditional(t, qT=0.1, rate=c(2, 1, 3), breakpoint=c(0.3, 0.8))
plot(t, F2_con, type='l', col='red', lwd=2, main="CDF and Quantile Function of
    Conditional \nPiecewsie Exp Dist", xlim=c(0, 1.2), ylim=c(0, 1.2))
lines(F2_con, qpwexp_conditional(F2_con, qT=0.1, rate=c(2, 1, 3),
    breakpoint=c(0.3,0.8)), lty=2, lwd=2, col='red')

# compare with CDF and quantile function of unconditional piecewise exp with rate 2, 1, 3
t <- seq(0, 1.2, 0.01)
F2 <- ppwexp(t, rate=c(2, 1, 3), breakpoint=c(0.3,0.8))
lines(t, F2, lwd=2)
lines(F2, qpwexp(F2, rate=c(2, 1, 3), breakpoint=c(0.3,0.8)), lty=2, lwd=2)
abline(v=0.1, col='grey')
abline(h=0.1, col='grey')
legend('topleft', c('CDF of piecewise exp dist given t > 0.1', 'quantile
    function of piecewise exp dist given t > 0.1', 'CDF of piecewise exp dist',
  'quantile function of piecewise exp dist'), col=c('red', 'red', 'black', 'black'),
  lty=c(1, 2, 1, 2), lwd=2)

# use rpwexp_conditional function to generate piecewise exp samples with rate 2, 1, 3 given t > 0.1
r_sample_con <- rpwexp_conditional(3000, qT=0.1, rate=c(2, 1, 3), breakpoint=c(0.3,0.8))
plot(ecdf(r_sample_con), col='red', lwd=2,  main="Empirical CDF of Conditional
    Piecewsie Exp Dist", xlim=c(0, 1.2), ylim=c(0, 1))

# compare with its CDF
lines(seq(0.1, 1.2, 0.01), F2_con, lwd=2)
legend('topleft', c('empirial CDF of piecewise exp dist given t > 0.1',
    'true CDF of piecewise exp dist given t > 0.1'), col=c('red', 'black'), lty=c(1,2), lwd=2)