# fnorm-distribution: Folded Normal Distribution In greybox: Toolbox for Model Building and Forecasting

## Description

Density, cumulative distribution, quantile functions and random number generation for the folded normal distribution with the location parameter mu and the scale sigma (which corresponds to standard deviation in normal distribution).

## Usage

 ```1 2 3 4 5 6 7``` ```dfnorm(q, mu = 0, sigma = 1, log = FALSE) pfnorm(q, mu = 0, sigma = 1) qfnorm(p, mu = 0, sigma = 1) rfnorm(n = 1, mu = 0, sigma = 1) ```

## Arguments

 `q` vector of quantiles. `mu` vector of location parameters (means). `sigma` vector of scale parameters. `log` if `TRUE`, then probabilities are returned in logarithms. `p` vector of probabilities. `n` number of observations. Should be a single number.

## Details

The distribution has the following density function:

f(x) = 1/sqrt(2 pi) (exp(-(x-mu)^2 / (2 sigma^2)) + exp(-(x+mu)^2 / (2 sigma^2)))

Both `pfnorm` and `qfnorm` are returned for the lower tail of the distribution.

## Value

Depending on the function, various things are returned (usually either vector or scalar):

• `dfnorm` returns the density function value for the provided parameters.

• `pfnorm` returns the value of the cumulative function for the provided parameters.

• `qfnorm` returns quantiles of the distribution. Depending on what was provided in `p`, `mu` and `sigma`, this can be either a vector or a matrix, or an array.

• `rfnorm` returns a vector of random variables generated from the fnorm distribution. Depending on what was provided in `mu` and `sigma`, this can be either a vector or a matrix or an array.

## Author(s)

Ivan Svetunkov, [email protected]

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10``` ```x <- dfnorm(c(-1000:1000)/200, 0, 1) plot(x, type="l") x <- pfnorm(c(-1000:1000)/200, 0, 1) plot(x, type="l") qfnorm(c(0.025,0.975), 0, c(1,2)) x <- rfnorm(1000, 0, 1) hist(x) ```

greybox documentation built on March 26, 2020, 7:32 p.m.