The hypoexponential distribution — hypoexponential • diseasy

Density, distribution, quantile and random generation functions for the hypoexponential distribution with parameters shape and rate.

Usage

dhypo(x, shape = 1, rate = rep(1, shape))

phypo(q, shape = 1, rate = rep(1, shape), lower.tail = TRUE)

qhypo(p, shape = 1, rate = rep(1, shape), lower.tail = TRUE)

rhypo(x, shape = 1, rate = rep(1, shape))

Arguments

x, q: vector of quantiles.
shape: (numeric(1))
shape parameter
rate: an alternative way to specify the scale.
lower.tail: logical; if TRUE (default), probabilities are \(P[X < x]\), otherwise, \(P[X \ge x]\) (exceptionally not cadlag here, to ensure, e.g., pgamma(0, shape=0) remains zero).
p: vector of probabilities.

Value

dhypo gives the density.
phypo gives the distribution function.
qhypo gives the quantile function.
rhypo gives the random generation.

Examples

  dhypo(1:10, shape = 2)
#>  [1] 0.3678794412 0.2706705665 0.1493612051 0.0732625556 0.0336897350
#>  [6] 0.0148725131 0.0063831738 0.0026837010 0.0011106882 0.0004539993
  dhypo(1:10, shape = 2, rate = c(1, 2))
#>  [1] 4.650883e-01 2.340393e-01 9.461663e-02 3.596035e-02 1.338509e-02
#>  [6] 4.945216e-03 1.822101e-03 6.707002e-04 2.467891e-04 9.079574e-05

  phypo(0.75, shape = 2)
#> [1] 0.1733585
  phypo(0.75, shape = 2, rate = c(1, 2))
#> [1] 0.2783971
  phypo(0.75, shape = 2, rate = c(1, 2), lower.tail = FALSE)
#> [1] 0.7216029

  qhypo(0.75, shape = 2)
#> [1] 2.692635
  qhypo(0.75, shape = 2, rate = c(1, 2))
#> [1] 2.010105
  qhypo(0.75, shape = 2, rate = c(1, 2), lower.tail = FALSE)
#> [1] 0.6931472

  rhypo(10, shape = 2)
#>  [1] 0.4012368 0.8040166 0.2945731 4.2924239 1.8912957 0.8239756 3.6207310
#>  [8] 0.7300902 0.6926275 0.7906260
  rhypo(10, shape = 2, rate = c(1, 2))
#>  [1] 2.5165786 1.1710231 0.2520009 0.5403438 2.0752860 0.6105865 1.0777397
#>  [8] 0.7228366 1.4876788 0.4501569