Reference · Statistics

stats.normal_pdf

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

What it does

The probability density of a normal distribution at x: the height of the bell curve there, as Python's NormalDist(mu, sigma).pdf(x). The mean mu is 0 and the standard deviation sigma 1 by default, the standard normal. A density is not a probability: it can be above 1 for a narrow curve, and the probability of a range is stats.normal_cdf at one end minus the other.

Examples

print(stats.normal_pdf(0))print(stats.normal_pdf(1), stats.normal_pdf(-1))print(stats.normal_pdf(100, 100, 15))

0.39894228040143270.24197072451914337 0.241970724519143370.02659615202676218

Edge cases

• The curve is symmetric about mu: pdf(mu + d) is pdf(mu - d).
• The peak at mu is 1 / (sigma * sqrt(2π)): a smaller sigma means a higher peak.
• Far from the mean the density is tiny but never 0.0.
• null for mu or sigma means the default.

print(stats.normal_pdf(0, 0, 2), stats.normal_pdf(0, 0, 0.1))print(stats.normal_pdf(0.5, null, 1) == stats.normal_pdf(0.5))print(stats.normal_pdf(10) > 0)

0.19947114020071635 3.989422804014327truetrue

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_pdf(0, 0, 0))

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

print(stats.normal_pdf("0"))

line 1: `stats.normal_pdf` expects a number as argument 1, got str

Chaining

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

print(1.5 | stats.normal_pdf | round(4))print([-1, 0, 1] | map((x) => stats.normal_pdf(x, 0, 1) | round(3)))print(115 | stats.normal_pdf(100, 15) | round(5))

0.1295[0.242, 0.399, 0.242]0.01613

See also

stats.normal_cdf, stats.normal_inv, stats.zscore

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