Chernoff tail bound for a Poisson count

\(P(S \ge (1+\epsilon)\lambda) \le \exp(-\lambda[(1+\epsilon)\log(1+\epsilon)-\epsilon])\) (Research.P7.Chernoff.poisson_chernoff), with a positive rate (rate_pos); the exact Poisson tail is returned beside it.

Usage

morie_poisson_chernoff(lambda, eps)

Arguments

lambda

Mean.

eps

Relative excess, positive.

Value

A data frame: eps, bound, exact, rate.

References

Grimmett G, Stirzaker D (2020). Probability and Random Processes, 4th ed., Theorem 5.11.4. Oxford.

Examples

morie_poisson_chernoff(lambda = 20, eps = c(0.25, 0.5, 1))
#>    eps        bound        exact       rate
#> 1 0.25 0.5606890625 1.567726e-01 0.02892944
#> 2 0.50 0.1148701128 2.181822e-02 0.10819766
#> 3 1.00 0.0004412552 5.320203e-05 0.38629436