Gaussbound: 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
An ordered vector containing the lower and upper bounds of the interval.
References
Pukelsheim, F. (1994) The Three Sigma Rule. The American Statistician48, 88-91.