Bernstein.p.value: Function to compute the p-value according to Bernstein...

In mosclust: Model Order Selection for Clustering

Function to compute the p-value according to Bernstein inequality.

Description

The Bernstein inequality gives an upper bound to the probability that the means of two random variables differ by chance, considering also their variance. This function implements the Berstein inequality and it is used by the functions Bernstein.compute.pvalues and Bernstein.ind.compute.pvalues

Usage

Bernstein.p.value(n, Delta, v)

Arguments

n	number of observations of the random variable
Delta	difference between the means
v	variance of the random variable

Value

a real number that provides an upper bound to the probability that the two means differ by chance

Author(s)

Giorgio Valentini [e-mail]

References

W. Hoeffding, Probability inequalities for sums of independent random variables, J. Amer. Statist. Assoc. vol.58 pp. 13-30, 1963.

See Also

Bernstein.compute.pvalues, Bernstein.ind.compute.pvalues

Examples

# Computation of the upper bounds to the probability that the two means differ by chance
Bernstein.p.value(n=100, Delta=0.1, v=0.01)
Bernstein.p.value(n=100, Delta=0.05, v=0.01)
Bernstein.p.value(n=100, Delta=0.05, v=0.1)
Bernstein.p.value(n=1000, Delta=0.05, v=0.1)

mosclust documentation built on June 8, 2025, 11:23 a.m.