# Cumulative distribution function¶

bdtr(k, n, p)

Returns the sum of the terms 0 through k of the Binomial probability density. The function is defined as:

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

See also bdtrc() and bdtri().

## Description¶

$\sum_{j=0}^k {n \choose j} p^j (1-p)^{n-j}$

The terms are not summed directly; instead the incomplete beta integral is employed, according to the formula:

y = bdtr(k, n, p) = incbet(n - k, k +1, 1 - p)


The arguments must be positive, with p ranging from 0 to 1.

## Accuracy¶

Tested at random points (a, b, p), with p between 0 and 1.

a, b   relative error
arithmetic domain # trials peak rms
For p between 0.001 and 1
IEEE 0, 100 100000 4.3e-15 2.6e-16

See also incbi().

## Error messages¶

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