Folded-binomial distribution for Bernoulli sample variances

Probability mass and tail probabilities for the folded count that determines the exact Bernoulli sample variance.

Usage

folded_binomial_pmf(v, m)

folded_binomial_tails(v, m)

Arguments

v

Bernoulli variance in [0, 1/4].

m

Arm sample size, at least 2.

Value

folded_binomial_pmf() returns a named probability vector over folded counts 0, ..., floor(m / 2). folded_binomial_tails() returns a list with lower and upper cumulative tail probabilities.

See also

Other rectangle helpers: binary_rectangle_corners(), cmr_multiarm_from_rectangle(), cmr_stratified_from_rectangle(), cmr_unbounded_from_rectangle(), multiarm_variance_objective(), rectangle_bernoulli_binary(), rectangle_bounded_two_arm(), rectangle_multiarm(), rectangle_multiple_outcomes(), rectangle_proxy(), rectangle_stratified(), rectangle_unbounded(), stratified_variance_objective(), variance_bounds_bernoulli_exact(), variance_bounds_maurer_pontil(), variance_bounds_unbounded_mom()

Examples

folded_binomial_pmf(v = 0.20, m = 8)
#>      0      1      2      3      4 
#> 0.0752 0.2304 0.3136 0.2688 0.1120 
folded_binomial_tails(v = 0.20, m = 8)
#> $lower
#>      0      1      2      3      4 
#> 0.0752 0.3056 0.6192 0.8880 1.0000 
#> 
#> $upper
#>      0      1      2      3      4 
#> 1.0000 0.9248 0.6944 0.3808 0.1120 
#>