Reference · Statistics

stats.normal_cdf

stats.normal_cdf(num, num=, num=) -> float

What it does

The cumulative probability of a normal distribution at x: the share of the distribution that lies at or below x, from 0 to 1, as Python's NormalDist(mu, sigma).cdf(x). The mean mu is 0 and the standard deviation sigma 1 by default, the standard normal. The probability of a range is the difference of two of them.

Examples

print(stats.normal_cdf(0))print(stats.normal_cdf(1.96), stats.normal_cdf(-1.96))print(stats.normal_cdf(130, 100, 15))print(stats.normal_cdf(1.96) - stats.normal_cdf(-1.96))

0.50.9750021048517796 0.0249978951482204280.97724986805182080.9500042097035593

Edge cases

• At mu it is exactly 0.5.
• Far below the mean it is 0.0 and far above 1.0; the float runs out of digits.
• It is the inverse of stats.normal_inv, up to the last digit.
• null for mu or sigma means the default.

print(stats.normal_cdf(7, 7, 3), stats.normal_cdf(-50), stats.normal_cdf(50))print(stats.normal_cdf(stats.normal_inv(0.3)))print(stats.normal_cdf(0, null, 2))

0.5 0.0 1.00.300000000000000040.5

Errors

A sigma of zero or below is a runtime error, not an error value. So is an argument that is not a number, or a missing x.

print(stats.normal_cdf(0, 0, -1))

line 1: `stats.normal_cdf`: sigma must be positive, got -1

print(stats.normal_cdf())

line 1: `stats.normal_cdf` expects a number as argument 1, got nothing

Chaining

In a pipeline x comes first and mu and sigma are the arguments:

print(1 | stats.normal_cdf | round(4))print(130 | stats.normal_cdf(100, 15) | round(3))print(1 - (130 | stats.normal_cdf(100, 15)) | round(3))

0.84130.9770.023

See also

stats.normal_inv, stats.normal_pdf, math.erf, stats.zscore

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