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Probability Density Functions for Probabilistic Uncertainty Analysis

Source: R/density.R
distributions.Rd

Define a distribution for PSA parameters.

Usage

normal(mean, sd)

lognormal(mean, sd, meanlog, sdlog)

gamma(mean, sd)

binomial(prob, size)

multinomial(...)

logitnormal(mu, sigma)

beta(shape1, shape2)

triangle(lower, upper, peak = (lower + upper)/2)

poisson(mean)

define_distribution(x)

beta(shape1, shape2)

triangle(lower, upper, peak = (lower + upper)/2)

use_distribution(distribution, smooth = TRUE)

Arguments

mean

Distribution mean.

sd

Distribution standard deviation.

meanlog

Mean on the log scale.

sdlog

SD on the log scale.

prob

Proportion.

size

Size of sample used to estimate proportion.

...

Dirichlet distribution parameters.

mu

Mean on the logit scale.

sigma

SD on the logit scale.

shape1

for beta distribution

shape2

for beta distribution

lower

lower bound of triangular distribution.

upper

upper bound of triangular distribution.

peak

peak of triangular distribution.

x

A distribution function, see details.

distribution

A numeric vector of observations defining a distribution, usually the output from an MCMC fit.

smooth

Use gaussian kernel smoothing?

Details

These functions are not exported, but only used in define_psa(). To specify a user-made function use define_distribution().

use_distribution() uses gaussian kernel smoothing with a bandwidth parameter calculated by stats::density(). Values for unobserved quantiles are calculated by linear interpolation.

define_distribution() takes as argument a function with a single argument, x, corresponding to a vector of quantiles. It returns the distribution values for the given quantiles. See examples.

Examples

define_distribution(
  function(x) stats::qexp(p = x, rate = 0.5)
)
#> [[1]]
#> function(x) stats::qexp(p = x, rate = 0.5)
#> <environment: 0x55e25a656c90>
#> 

# a mixture of 2 gaussians
x <- c(rnorm(100), rnorm(100, 6))
plot(density(x))


use_distribution(x)
#> [[1]]
#> function (x) 
#> {
#>     if (smooth) {
#>         noise <- stats::rnorm(n = length(x), mean = 0, sd = stats::density(distribution)$bw)
#>     }
#>     else {
#>         noise <- 0
#>     }
#>     (stats::approxfun(x = seq(0, 1, length = length(distribution)), 
#>         y = distribution))(x) + noise
#> }
#> <bytecode: 0x55e25a3e2da8>
#> <environment: 0x55e25a3e3dd8>
#>