Python commands for dealing with the normal distribution

audrey

In this recent forum assignment, we are asked to compute a $(100-s)\%$ confidence interval. How can we use the computer to find the correct $z^*$ multiplier? More generally, what kinds of commands does Python provide to deal with the normal distribution?

mark

To access commands for the normal distribution, first execute the following:

from scipy.stats import norm

Now, the norm object has a bunch of methods - three of which are immediately relevant for us:

• norm.pdf (the Probability Distribution function),
• norm.cdf (the Cumulative Distribution function), and
• norm.ppf (The Point Percentile Function)

We can see the geometric relevance of these in the following picture:

Note that the PDF function tells us the value of the probability distribution function, i.e. the $y$-coordinate or $0.1295$ in this case. The CDF function tells us how much area has accumulated under the function. The PPF function is the inverse of the CDF function. Thus, it tells us what $z$ value you want to accumulate a specified amount of area. PPF is exactly what you need to find a $z^*$ multiplier.

[
  norm.pdf(1.5),
  norm.cdf(1.5),
  norm.ppf(0.9331927987)
]

# Out:
# [0.12951759566589174, 0.9331927987311419, 1.4999999997595546]