The probability of a given value in a multivariate Gaussian distribution is calculated as follows:
- Import the relevant packages:
from scipy.stats import multivariate_normal
import numpy as np
- Initialize the array of variables:
x = np.array([[1,2], [3,4]])
In the preceding code snippet, we have initialized two data points located in a two-dimensional space.
- Calculate the probability associated with the two data points using the pdf function, where the mean and variance along the two dimensions is given, as follows:
multivariate_normal.pdf(x, mean=[0, 1], cov=[5, 2])
array([ 0.0354664 , 0.00215671])
The output of the preceding code results in probabilities associated with the first data point [1, 2] and the second data point [3, 4].
Obtaining random samples of a distribution
Random numbers can be generated using multiple functions within numpy.random.
The following table lists the set of functions that are used to generate random data:
|
Function |
Working |
Example |
|
Rand |
Returns random values in a given shape |
numpy.random.rand(2,2) |
|
Randn |
Returns a sample (or samples) from the standard normal distribution |
numpy.random.randn(2,2) |
|
Randint |
Returns random integers from low (inclusive) to high (exclusive) |
numpy.random.randint(2,20,5) |
|
Random_integers |
Returns random integers of np.int type among low, high, and inclusive |
numpy.random.random_integers(2,20,5) |
|
Random |
Returns random floats in the half-open interval [0.0, 1.0) |
numpy.random.random(5) |
A list of all the possible distributions from which random samples can be drawn is as follows:
|
Function |
Working |
|
beta(a, b[, size]) |
Draws samples from a beta distribution |
|
binomial(n, p[, size]) |
Draws samples from a binomial distribution |
|
chisquare(df[, size]) |
Draws samples from a chi-square distribution |
|
dirichlet(alpha[, size]) |
Draws samples from the Dirichlet distribution |
|
exponential([scale, size]) |
Draws samples from an exponential distribution |
|
f(dfnum, dfden[, size]) |
Draws samples from an F distribution |
|
gamma(shape[, scale, size]) |
Draws samples from a gamma distribution |
|
geometric(p[, size]) |
Draws samples from the geometric distribution |
|
gumbel([loc, scale, size]) |
Draws samples from a Gumbel distribution |
|
hypergeometric(ngood, nbad, nsample[, size]) |
Draws samples from a hypergeometric distribution |
|
laplace([loc, scale, size]) |
Draws samples from the Laplace or double exponential distribution with a specified location (or mean) and scale (decay) |
|
logistic([loc, scale, size]) |
Draws samples from a logistic distribution |
|
lognormal([mean, sigma, size]) |
Draws samples from a log-normal distribution |
|
logseries(p[, size]) |
Draws samples from a logarithmic series distribution |
|
multinomial(n, pvals[, size]) |
Draws samples from a multinomial distribution |
|
multivariate_normal(mean, cov[, size, ...) |
Draws random samples from a multivariate normal distribution |
|
negative_binomial(n, p[, size]) |
Draws samples from a negative binomial distribution |
|
noncentral_chisquare(df, nonc[, size]) |
Draws samples from a noncentral chi-square distribution |
|
noncentral_f(dfnum, dfden, nonc[, size]) |
Draws samples from the noncentral F distribution |
|
normal([loc, scale, size]) |
Draws random samples from a normal (Gaussian) distribution |
|
pareto(a[, size]) |
Draws samples from a Pareto II or Lomax distribution with a specified shape |
|
poisson([lam, size]) |
Draws samples from a Poisson distribution |
|
power(a[, size]) |
Draws samples in [0, 1] from a power distribution with a positive exponent, a - 1 |
|
rayleigh([scale, size]) |
Draws samples from a Rayleigh distribution |
|
standard_cauchy([size]) |
Draws samples from a standard Cauchy distribution with mode = 0 |
|
standard_exponential([size]) |
Draws samples from the standard exponential distribution |
|
standard_gamma(shape[, size]) |
Draws samples from a standard gamma distribution |
|
standard_normal([size]) |
Draws samples from a standard normal distribution (mean=0, stdev=1) |
|
standard_t(df[, size]) |
Draws samples from a standard Student's T distribution with df degrees of freedom |
|
triangular(left, mode, right[, size]) |
Draws samples from the triangular distribution over the interval [left, right] |
|
uniform([low, high, size]) |
Draws samples from a uniform distribution |
|
vonmises(mu, kappa[, size]) |
Draws samples from a von Mises distribution |
|
wald(mean, scale[, size]) |
Draws samples from a Wald or inverse Gaussian distribution |
|
weibull(a[, size]) |
Draws samples from a Weibull distribution |
|
zipf(a[, size]) |
Draws samples from a Zipf distribution |
Given all the preceding functions to generate certain distributions, in order to understand how to generate random samples in a given distribution in Python, we will go through it in the following code:
- Import the relevant packages:
import numpy.random
- Generate 10 random numbers from a standard normal distribution:
numpy.random.standard_normal(10)
The preceding code generates the following output:
array([ 1.19322748, 0.15660068, 0.16968799, -0.9599914 , -1.60431604,
0.31921513, -0.26443506, 1.2290333 , 1.10691107, -0.23452172])