# Inverse of the cumulative distribution function¶

bdtri(k, n, y)

Finds the event probability p such that the sum of the terms 0 through k of the Binomial probability density is equal to the given cumulative probability y.

Parameters: k (int) – number of successes within [0, n] n (int) – number of trials y (float) – cumulative probability within [0, 1]

See also bdtr() and bdtrc().

## Description¶

This is accomplished using the inverse beta integral function and the relation:

1 - p = incbi(n - k, k + 1, y)


## Accuracy¶

Tested at random points (a, b, p).

a, b   relative error
arithmetic domain # trials peak rms
For p between 0.001 and 1
IEEE 0, 100 100000 2.3e-14 6.4e-16
IEEE 0, 10000 100000 6.6e-12 1.2e-13
For p between 10^-6 and 0.001
IEEE 0, 100 100000 2.0e-12 1.3e-14
IEEE 0, 10000 100000 1.5e-12 3.2e-14

See also incbi().

## Error messages¶

message condition value returned
bdtri domain k < 0, n <= k 0.0
x < 0, x > 1