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

Reference: http://www.netlib.org/cephes/doubldoc.html#bdtr