Functions to compute the probability density function, cumulative distribution function, and quantile function for the Gamma distribution.
Usage
gamma_distribution(shape, scale = 1)
gamma_pdf(x, shape, scale = 1)
gamma_lpdf(x, shape, scale = 1)
gamma_cdf(x, shape, scale = 1)
gamma_lcdf(x, shape, scale = 1)
gamma_quantile(p, shape, scale = 1)Value
A single numeric value with the computed probability density, log-probability density, cumulative distribution, log-cumulative distribution, or quantile depending on the function called.
See also
Boost Documentation for more details on the mathematical background.
Examples
# Gamma distribution with shape = 3, scale = 4
dist <- gamma_distribution(3, 4)
# Apply generic functions
cdf(dist, 0.5)
#> [1] 0.0002964775
logcdf(dist, 0.5)
#> [1] -8.123539
pdf(dist, 0.5)
#> [1] 0.001723627
logpdf(dist, 0.5)
#> [1] -6.363325
hazard(dist, 0.5)
#> [1] 0.001724138
chf(dist, 0.5)
#> [1] 0.0002965215
mean(dist)
#> [1] 12
median(dist)
#> [1] 10.69624
mode(dist)
#> [1] 8
range(dist)
#> [1] 0.000000e+00 1.797693e+308
quantile(dist, 0.2)
#> [1] 6.140177
standard_deviation(dist)
#> [1] 6.928203
support(dist)
#> [1] 2.225074e-308 1.797693e+308
variance(dist)
#> [1] 48
skewness(dist)
#> [1] 1.154701
kurtosis(dist)
#> [1] 5
kurtosis_excess(dist)
#> [1] 2
# Convenience functions
gamma_pdf(2, 3, 4)
#> [1] 0.01895408
gamma_lpdf(2, 3, 4)
#> [1] -3.965736
gamma_cdf(2, 3, 4)
#> [1] 0.01438768
gamma_lcdf(2, 3, 4)
#> [1] -4.241383
gamma_quantile(0.5, 3, 4)
#> [1] 10.69624