Reference · Statistics

stats.normal_inv

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

What it does

The inverse of stats.normal_cdf: the x below which a share p of a normal distribution lies, with p strictly between 0 and 1, as Python's NormalDist(mu, sigma).inv_cdf(p) (Wichura's algorithm AS241). The mean mu is 0 and the standard deviation sigma 1 by default, the standard normal. It gives the critical values of tests and the cut points of confidence intervals.

Examples

print(stats.normal_inv(0.5))print(stats.normal_inv(0.975), stats.normal_inv(0.025))print(stats.normal_inv(0.9, 100, 15))

0.01.9599639845400536 -1.9599639845400538119.22327348316901

Edge cases

• p of 0 or 1 is an error, not infinity: the tails never end.
• A p very close to 0 or 1 is fine; 1e-300 gives about -37.
• It is symmetric: inv(1 - p) is -inv(p) about mu, up to the last digit.
• null for mu or sigma means the default.

print(stats.normal_inv(1e-300), stats.normal_inv(0.999999))print(stats.normal_inv(0.5, 7, 3), stats.normal_inv(0.84, null, null))print(stats.normal_inv(stats.normal_cdf(1.5)))

-37.0470962993612 4.7534243088170897.0 0.99445788320975281.4999999999999998

Errors

A p of 0, 1, or outside them is a runtime error, not an error value. So are a sigma of zero or below and an argument that is not a number.

print(stats.normal_inv(0))

line 1: `stats.normal_inv`: p must be between 0 and 1 (exclusive), got 0

print(stats.normal_inv(1))

line 1: `stats.normal_inv`: p must be between 0 and 1 (exclusive), got 1

print(stats.normal_inv(0.5, 0, 0))

line 1: `stats.normal_inv`: sigma must be positive, got 0

Chaining

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

print(0.975 | stats.normal_inv | round(3))print(0.95 | stats.normal_inv(100, 15) | round(1))print([0.025, 0.5, 0.975] | map((p) => stats.normal_inv(p) | round(2)))

1.96124.7[-1.96, 0.0, 1.96]

See also

stats.normal_cdf, stats.normal_pdf, stats.percentile

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