Density Function of Truncated Piecewise Exponential Distribution

Obtains the density of a truncated piecewise exponential distribution.

Usage

dtpwexp(
  q,
  piecewiseSurvivalTime = 0,
  lambda = 0.0578,
  lowerBound = 0,
  log.d = FALSE
)

Arguments

q

The vector of quantiles.

piecewiseSurvivalTime

A vector that specifies the starting time of piecewise exponential survival time intervals. Must start with 0, e.g., c(0, 6) breaks the time axis into 2 event intervals: \([0, 6)\) and \([6, \infty)\). Defaults to 0 for exponential distribution.

lambda

A vector of hazard rates for the event. One for each analysis time interval.

lowerBound

The left truncation time point for the survival time. Defaults to 0 for no truncation.

log.d

Logical; if TRUE, densities d are given as log(d).

Value

The density d such that d = lambda(q) * P(X > q | X > lowerBound).

Author

Kaifeng Lu, kaifenglu@gmail.com

Examples

dtpwexp(q = c(8, 18), piecewiseSurvivalTime = c(0, 6, 9, 15),
        lambda = c(0.025, 0.04, 0.015, 0.007))
#> [1] 0.031781344 0.004782245