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

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