# distributions: Probability Density Functions for Probabilistic Uncertainty... In pierucci/heemod: Markov Models for Health Economic Evaluations

## Description

Define a distribution for PSA parameters.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25``` ```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 bandwith 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

 ```1 2 3 4 5 6 7 8 9``` ```define_distribution( function(x) stats::qexp(p = x, rate = 0.5) ) # a mixture of 2 gaussians x <- c(rnorm(100), rnorm(100, 6)) plot(density(x)) use_distribution(x) ```

pierucci/heemod documentation built on July 15, 2018, 12:44 p.m.