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:
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 |