The Gamma Distribution

Density, distribution function, quantile function and random generation for the Gamma distribution with parameters shape and scale.

Usage

pgamma2(
  q,
  mean,
  sd = sqrt(mean),
  lower.tail = TRUE,
  log.p = FALSE,
  convex = TRUE
)

Arguments

q

vector of quantiles

mean

the mean value on the true scale (vectorised)

sd

the standard deviation on the true scale (vectorised)

lower.tail

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

log.p

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

convex

Show a warning if the distribution selected is not a convex function

Value

dgamma gives the density, pgamma gives the distribution function, qgamma gives the quantile function, and rgamma generates random deviates.

Invalid arguments will result in return value NaN, with a warning.

The length of the result is determined by n for rgamma, and is the maximum of the lengths of the numerical arguments for the other functions.

The numerical arguments other than n are recycled to the length of the result. Only the first elements of the logical arguments are used.

See also

stats::pgamma()

Examples

pgamma2(seq(0,4,0.25), 2, 1)
#>  [1] 0.000000000 0.001751623 0.018988157 0.065642454 0.142876540 0.242423867
#>  [7] 0.352768111 0.463367332 0.566529880 0.657704044 0.734974085 0.798300801
#> [13] 0.848796117 0.888150388 0.918234584 0.940854540 0.957619888