# kappa4IntApprox: Sample arc length statistic. In alR: Arc Lengths of Statistical Functions

## Description

The arc length over a specified interval is calculated for use in non-linear estimation.

## Usage

 ```1 2 3``` ```kappa4IntApprox(x, y, q1, q2, quantile) kappa4IntApprox2(x, y, q1, q2, quantile) ```

## Arguments

 `x` Numeric vector of independent outcomes. `y` Numeric vector of dependent outcomes y=F(x). `q1, q2` Quantiles (between 0 and 1) over which the arc length segment is to be computed. `quantile` Logical, TRUE/FALSE, whether `q1` and `q2` are quantiles, or actual points in the domain.

## Value

kappa4IntApprox: The resultant arc length.

kappa4IntApprox2: A vector having length equal to that of the vector of lower quantile bounds, containing the discrete arc length segments over the specified intervals.

## Examples

 ```1 2 3 4 5 6 7``` ```x <- rnorm(100) y <- pnorm(x) kappa4IntApprox(x, y, 0.025, 0.975, TRUE) kappa4IntApprox(x, y, -1.96, 1.96, FALSE) kappa4IntApprox2(x, y, c(0.025, 0.5), c(0.5, 0.975), TRUE) kappa4IntApprox2(x, y, c(-1.96, 0), c(0, 1.96), FALSE) ```

alR documentation built on Dec. 7, 2017, 5:03 p.m.