Gaussbound {regspec}

Compute the Gauss bounds for a random variable.

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

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

bounds

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

Author(s)

Ben Powell

References

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

Examples

Gaussbound(1,1,0.9)