# Numpy Distributions and Statistical Functions: Examples + Reference

Last updated:

imports:all examples assume you have the following at the top of your script:`import numpy as np`

and`import scipy.stats as st`

## Random sampling from a distribution

In general, leave out the

`size=`

parameter if you just want a sample with a single element

Draw 10 samples from a

**standard**normal distribution`# mean at zero and standard deviation of 1 np.random.randn(10) # array([ 0.32929561, -0.5814358 , 0.74105779, 0.06120152, 1.02753804, # 0.2814268 , 0.76394055, -0.13202086, -0.99976205, -0.51692293])`

Draw 10 samples from an arbitrary normal distribution

`# an array of 10 points randomly sampled from a normal distribution # loc=mean, scale=std deviation np.random.normal(loc=0.0, scale=1.0, size=10) # array([ 0.57258901, 2.25547575, 0.65749017, -0.04182533, 0.55000601, # -1.15594624, 0.32455692, 0.16460812, 0.70899117, -0.95861313])`

Draw 10 samples from an uniform distribution

`np.random.uniform(low=0,high=1,size=10) # array([ 0.21310048, 0.28180847, 0.58721479, 0.8013283 , 0.33171448, # 0.98888729, 0.4519467 , 0.93362951, 0.64370449, 0.13997242])`

Draw 10 integers from a uniform distribution (discrete) between 0 and 100

`np.random.randint(low=0, high=100, size=10) # array([92, 95, 57, 6, 26, 86, 55, 46, 29, 62])`

if you want draws

**without**replacement, do this instead:`# the only difference is that this will return samples from # 0 to 99 (100 is the size of the range) np.random.choice(100,10,replace=False)`

## Draw from collections

Draw 1 element from a given array:

`elem = np.random.choice([0,1]) # elem has 0.5 chance of being 0 or 1`

## Evaluate x on a PDF

Standard normal (Gaussian) distribution

I.e. P(x) | P ~ Gaussian(0,1)

`dist = st.norm(loc=0.0,scale=1.0) dist.pdf(1.645) # 0.10311081109198142`

## Evaluate x on a CDF

Standard normal (Gaussian) distribution

I.e. What percentage of the density is to the left of x?

`dist = st.norm(loc=0.0,scale=1.0) dist.cdf(1.645) # 0.95001509446087862`