Inverse Gamma Distribution Functions
Source:R/inverse_gamma_distribution.R
inverse_gamma_distribution.RdFunctions to compute the probability density function, cumulative distribution function, and quantile function for the Inverse Gamma distribution.
With shape \(\alpha\) and scale \(\beta\), the PDF is
$$f(x;\alpha,\beta) = \frac{\beta^{\alpha}}{\Gamma(\alpha)} x^{-\alpha-1} \exp\left(-\frac{\beta}{x}\right)$$
The CDF is $$F(x;\alpha,\beta)=\Gamma(\alpha,\beta/x)/\Gamma(\alpha)$$
Usage
inverse_gamma_distribution(shape, scale = 1)
inverse_gamma_pdf(x, shape, scale = 1)
inverse_gamma_lpdf(x, shape, scale = 1)
inverse_gamma_cdf(x, shape, scale = 1)
inverse_gamma_lcdf(x, shape, scale = 1)
inverse_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
# Inverse Gamma distribution with shape = 5, scale = 4
dist <- inverse_gamma_distribution(5, 4)
# Apply generic functions
cdf(dist, 0.5)
#> [1] 0.0996324
logcdf(dist, 0.5)
#> [1] -2.306268
pdf(dist, 0.5)
#> [1] 0.9160366
logpdf(dist, 0.5)
#> [1] -0.08769894
hazard(dist, 0.5)
#> [1] 1.017403
chf(dist, 0.5)
#> [1] 0.1049522
mean(dist)
#> [1] 1
median(dist)
#> [1] 0.8563644
mode(dist)
#> [1] 0.6666667
range(dist)
#> [1] 0.000000e+00 1.797693e+308
quantile(dist, 0.2)
#> [1] 0.5951514
standard_deviation(dist)
#> [1] 0.5773503
support(dist)
#> [1] 0.000000e+00 1.797693e+308
variance(dist)
#> [1] 0.3333333
skewness(dist)
#> [1] 3.464102
kurtosis(dist)
#> [1] 45
kurtosis_excess(dist)
#> [1] 42
# Convenience functions
inverse_gamma_pdf(2, 5, 4)
#> [1] 0.09022352
inverse_gamma_lpdf(2, 5, 4)
#> [1] -2.405465
inverse_gamma_cdf(2, 5, 4)
#> [1] 0.947347
inverse_gamma_lcdf(2, 5, 4)
#> [1] -0.05408985
inverse_gamma_quantile(0.5, 5, 4)
#> [1] 0.8563644