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

Usage

landau_distribution(location = 0, scale = 1)

landau_pdf(x, location = 0, scale = 1)

landau_lpdf(x, location = 0, scale = 1)

landau_cdf(x, location = 0, scale = 1)

landau_lcdf(x, location = 0, scale = 1)

landau_quantile(p, location = 0, scale = 1)

Arguments

location

location parameter (default is 0)

scale

scale parameter (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

# Landau distribution with location 0 and scale 1
dist <- landau_distribution(0, 1)
# Apply generic functions
cdf(dist, 0.5)
#> [1] 0.4842393
logcdf(dist, 0.5)
#> [1] -0.7251762
pdf(dist, 0.5)
#> [1] 0.2123185
logpdf(dist, 0.5)
#> [1] -1.549668
hazard(dist, 0.5)
#> [1] 0.4116608
chf(dist, 0.5)
#> [1] 0.6621123
median(dist)
#> [1] 0.5756301
mode(dist)
#> [1] -0.4293145
range(dist)
#> [1] -Inf  Inf
quantile(dist, 0.2)
#> [1] -0.5948319
support(dist)
#> [1] -Inf  Inf

# Convenience functions
landau_pdf(3)
#> [1] 0.05863949
landau_lpdf(3)
#> [1] -2.836347
landau_cdf(3)
#> [1] 0.7792967
landau_lcdf(3)
#> [1] -0.2493635
landau_quantile(0.5)
#> [1] 0.5756301