Cumulative probability: gamma distribution constrained to have mean > sd

The following conversion describes the parameters mean and kappa

Usage

pcgamma(q, mean, kappa = 1/mean, lower.tail = TRUE, log.p = FALSE)

Arguments

q

vector of quantiles

mean

the mean value on the true scale (vectorised)

kappa

a coefficient of variation. where 0 is no variability and 1 is maximally variability (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).

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.

Details

$$ \text{shape:} \alpha = \frac{1}{\kappa} \\ \text{rate:} \beta = \frac{1}{\mu \times \kappa} \\ \text{scale:} \sigma = \mu \times \kappa \\ $$

See also

stats::pgamma()

Examples

pcgamma(seq(0,4,0.25), 2, 0.5)
#>  [1] 0.00000000 0.02649902 0.09020401 0.17335853 0.26424112 0.35536421
#>  [7] 0.44217460 0.52212166 0.59399415 0.65745252 0.71270250 0.76027052
#> [13] 0.80085173 0.83520962 0.86411177 0.88829071 0.90842181