Inverse Gaussian Distribution Functions

Functions to compute the probability density function, cumulative distribution function, and quantile function for the Inverse Gaussian distribution.

Usage

inverse_gaussian_distribution(mu = 1, lambda = 1)

inverse_gaussian_pdf(x, mu = 1, lambda = 1)

inverse_gaussian_lpdf(x, mu = 1, lambda = 1)

inverse_gaussian_cdf(x, mu = 1, lambda = 1)

inverse_gaussian_lcdf(x, mu = 1, lambda = 1)

inverse_gaussian_quantile(p, mu = 1, lambda = 1)

Arguments

mu

mean parameter (mu > 0; default is 1)

lambda

scale parameter (lambda > 0; default is 1)

x

quantile

p

probability (0 <= p <= 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 Gaussian distribution with mu = 3, lambda = 4
dist <- inverse_gaussian_distribution(3, 4)
# Apply generic functions
cdf(dist, 0.5)
#> [1] 0.01617264
logcdf(dist, 0.5)
#> [1] -4.124435
pdf(dist, 0.5)
#> [1] 0.1403174
logpdf(dist, 0.5)
#> [1] -1.963848
hazard(dist, 0.5)
#> [1] 0.142624
chf(dist, 0.5)
#> [1] 0.01630484
mean(dist)
#> [1] 3
median(dist)
#> [1] 2.202698
mode(dist)
#> [1] 1.140598
range(dist)
#> [1]  0.000000e+00 1.797693e+308
quantile(dist, 0.2)
#> [1] 1.161488
standard_deviation(dist)
#> [1] 2.598076
support(dist)
#> [1]  0.000000e+00 1.797693e+308
variance(dist)
#> [1] 6.75
skewness(dist)
#> [1] 2.598076
kurtosis(dist)
#> [1] 8.25
kurtosis_excess(dist)
#> [1] 11.25

# Convenience functions
inverse_gaussian_pdf(2, 3, 4)
#> [1] 0.2524295
inverse_gaussian_lpdf(2, 3, 4)
#> [1] -1.376623
inverse_gaussian_cdf(2, 3, 4)
#> [1] 0.4512408
inverse_gaussian_lcdf(2, 3, 4)
#> [1] -0.7957542
inverse_gaussian_quantile(0.5, 3, 4)
#> [1] 2.202698