# Gaussbound: Compute the Gauss bounds for a random variable. In regspec: Non-Parametric Bayesian Spectrum Estimation for Multirate Data

## Description

This is a simple function that computes bounds for a credible interval according to Gauss's inequality. If a random variable has a Lebesgue density with a single mode (`mode`) and a finite expected squared deviation (`tau`^2) from this mode, then Gauss's inequality tells us that at least a given proportion (`prob`) of the distribution's mass lies within a finite symmetric interval centred on the mode.

## Usage

 `1` ```Gaussbound(mode, tau, prob) ```

## Arguments

 `mode` Numeric. The location of the density's mode. `tau` Numeric. The square root of the expected squared deviation from the mode. `prob` Numeric. A lower bound on the probability mass that is contained within the interval

## Value

 ` ` An ordered vector containing the lower and upper bounds of the interval.

Ben Powell

## References

Pukelsheim, F. (1994) The Three Sigma Rule. The American Statistician 48, 88-91.

## Examples

 `1` ```Gaussbound(1,1,0.9) ```

regspec documentation built on May 29, 2017, 6:53 p.m.