# totalvariation.circular: Conditional total variation distance between two circular... In circular: Circular Statistics

## Description

The total variation distance between two circular samples is evaluated conditional on a circular modal region.

## Usage

 ```1 2 3``` ```totalvariation.circular(x, y, z = NULL, q = 0.95, bw, adjust = 1, type = c("K", "L"), kernel = c("vonmises", "wrappednormal"), na.rm = FALSE, step = 0.001, eps.lower = 10^(-4), eps.upper = 10^(-4), ...) ```

## Arguments

 `x` numeric or an object of class `circular`. `y` numeric or an object of class `circular`. `z` numeric or object of class `circular`. The grid were the kernel density estimate will be evaluated. If `NULL` equally spaced points in the interval [0,2*pi) with step `step`. `q` numeric in the interval [0,1]. The quantile of the modal region. `bw` the smoothing bandwidth to be used. When the `kernel` is `vonmises` the bandwidth is equal to the concentration parameter. `adjust` the bandwidth used is actually `adjust*bw`. This makes it easy to specify values like “half the default bandwidth”. `type` Not Yet Used. `kernel` a character string giving the smoothing kernel to be used. This must be one of `"vonmises"` or `"wrappednormal"`, that are kernels of `type` `"K"`. `na.rm` logical; if `TRUE`, missing values are removed from `x`. If `FALSE` any missing values cause an error. `step` numeric. Used in the construction of the regular grid `z`. `eps.lower,eps.upper` the cut point in the density is searched in the interval [min(density)*(1+eps.lower),max(density)*(1-eps.upper)]. `...` further arguments passed to the `modal.region.circular` function. Not used at present.

## Value

A list of class `totalvariation.circular` with the following components

 `tv` the (conditional) total variation. `ovl` the (conditional) overlapping coefficient. `q` the order of the modal regions. `bw` the bandwidth value as in input. `modal.x` an obejct of class `modal.region.circular` for the `x` data set. `modal.y` an obejct of class `modal.region.circular` for the `y` data set. `density.x` an obejct of class `density.circular` for the `x` data set. `density.y` an obejct of class `density.circular` for the `y` data set. `density` a function which report the positive part of the difference between the estimated density of the two data sets.

## Author(s)

Claudio Agostinelli

## References

L.G.R. Oliveira-Santos, C.A. Zucco and C. Agostinelli (2013) Using conditional circular kernel density functions to test hypotheses on animal circadian activity. Animal Behaviour, 85(1) 269-280.

`modal.region.circular`
 ```1 2 3 4``` ```x <- rvonmises(100, circular(pi), 10) y <- rvonmises(100, circular(pi+pi/8), 10) res <- totalvariation.circular(x,y,bw=50) plot(res) ```