# sm.density.compare: Comparison of univariate density estimates In sm: Smoothing Methods for Nonparametric Regression and Density Estimation

## Description

This function allows a set of univariate density estimates to be compared, both graphically and formally in a permutation test of equality.

## Usage

 `1` ```sm.density.compare(x, group, h, model = "none", ...) ```

## Arguments

 `x` a vector of data. `group` a vector of group labels. `h` the smoothing parameter to be used in the construction of each density estimate. Notice that the same smoothing parameter is used for each group. If this value is omitted, the mean of the normal optimal values for the different groups is used. `model` the default value is `"none"` which restricts comparison to plotting only. The alternative value `"equal"` can produce a bootstrap hypothesis test of equality and the display of an appropriate reference band. `...` other optional parameters are passed to the `sm.options` function, through a mechanism which limits their effect only to this call of the function. Those specifically relevant for this function are the following: `method`, `df`, `band`, `test`, `nboot`, plus those controlling graphical display (unless `display="none"` is set); see the documentation of `sm.options` for their description. The parameter `nboot` controls teh number of permutations used in the permutation test.

## Details

see Section 6.2 of the reference below.

## Value

When `model` is set to `"none"`, nothing is returned. When `"model"` is set to `"equal"`, a list containing the smoothing parameter and the p-value of the test is returned. When `band` takes the value `TRUE`, and there are only two groups to compare, the list contains in addition the upper and lower end-points of the reference band for equality.

## Side Effects

a plot on the current graphical device is produced, unless `display="none"`.

## References

Bowman, A.W. and Azzalini, A. (1997). Applied Smoothing Techniques for Data Analysis: the Kernel Approach with S-Plus Illustrations. Oxford University Press, Oxford.

## See Also

`sm.density`, `sm.ancova`, `sm.options`

## Examples

 ```1 2 3``` ```y <- rnorm(100) g <- rep(1:2, rep(50,2)) sm.density.compare(y, g, model="equal") ```

### Example output ```Package 'sm', version 2.2-5.6: type help(sm) for summary information
Warning message:
no DISPLAY variable so Tk is not available

Test of equal densities:  p-value =  0.36
```

sm documentation built on May 1, 2019, 8:06 p.m.