# intersect.modal.region: Intersection between model region and a given interval. In circular: Circular Statistics

## Description

Find an estimates of the probability of the intersection between a modal region and a given interval.

## Usage

 ```1 2 3 4 5 6 7``` ```intersect.modal.region(x, ...) ## Default S3 method: intersect.modal.region(x, ...) ## S3 method for class 'circular' intersect.modal.region(x, breaks, z = NULL, q = 0.95, bw, adjust = 1, type = c("K", "L"), kernel = c("vonmises", "wrappednormal"), na.rm = FALSE, step = 0.01, eps.lower = 10^(-4), eps.upper = 10^(-4), ...) ```

## Arguments

 `x` numeric or an object of class `circular`. `breaks` a matrix with two columns. Each row specifies a sub-interval. `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 next methods.

## Details

Only the version for circular data is actually implemented.

## Value

For the circular method a list with the following three components

 `tot` the total area. `areas` information for each subinterval. `breaks` the extremes of each subinterval.

## Author(s)

Claudio Agostinelli

`modal.region`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ``` x <- rvonmises(100, circular(pi), 10) res <- intersect.modal.region(x, breaks=circular(matrix(c(pi,pi+pi/12, pi-pi/12, pi), ncol=2, byrow=TRUE)), bw=50) res\$tot x <- rvonmises(100, circular(0), 10) res <- intersect.modal.region(x, breaks=circular(matrix(c(pi,pi+pi/12), ncol=2)), bw=50) res\$tot res <- intersect.modal.region(x, breaks=circular(matrix(c(pi/12, 2*pi-pi/12), ncol=2, byrow=TRUE)), bw=50) res\$tot ```