# normal: Functions for generating and fitting named distribution... In robertdouglasmorrison/DuffyTools: Duffy Lab Utility Tools

## Description

Generate or fit by nonlinear least squares a family of classic distribution functions.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```normal(x, mean = 0, sd = 1, height = NULL, floor = 0) fit.normal(x, y, start.mean = 0, start.sd = 1, start.height = NULL, start.floor = 0) gaussian(x, center = 0, width = 1, height = NULL, floor = 0) fit.gaussian(x, y, start.center = 0, start.width = 1, start.height = NULL, start.floor = 0) lorentzian(x, center = 0, width = 1, height = NULL, floor = 0) fit.lorentzian(x, y, start.center = 0, start.width = 1, start.height = NULL, start.floor = 0) gumbel(x, center = 0, width = 1, height = NULL, floor = 0) fit.gumbel(x, y, start.center = 0, start.width = 1, start.height = NULL, start.floor = 0) ```

## Arguments

 `x` a vector of values to evaluate or fit the function at `y` a vector of observed Y values to fit the named distribution to `mean, center` the central value for the function `sd, width` the nominal measure of the width of the distribution. Note that this is a signed value for gumbel distributions, affecting the direction of the asymmetric tail. `height` an optional multiplier for adjusting the magnitude of the Y values returned. By default, the height is defined by the underlying function. `floor` an optional floor value for the tails of the distribution. This has the effect of applying a linear offset to the Y values. `start.center, start.width, start.height, etc.` for the `fit.` functions, optional starting estimates passed to the NLS routine. See `nls`. to the Y values.

## Value

For the curve generation functions, a vector of Y values, from evaluating the function at all values in X.

For the curve fitting functions, a list containing:

 `y ` a vector of best fit values of Y, at each location in X. `mean,center ` the best fit curve parameter of the distribution's central value. `sd,width ` the best fit curve parameter of the distribution's width. `height ` the best fit curve parameter of the distribution's height. `floor ` if fitted, the best fit curve parameter of the distribution's floor (linear offset of the function tails)

## Note

While the functions are implemented differently, 'normal' an 'gaussian' are effectively the same.

## Author(s)

Bob Morrison

robertdouglasmorrison/DuffyTools documentation built on Dec. 7, 2018, 8:02 a.m.