numpy.random() in Python

The random is a module present in the NumPy library. This module contains the functions which are used for generating random numbers. This module contains some simple random data generation methods, some permutation and distribution functions, and random generator functions.

All the functions in a random module are as follows:

Simple random data

There are the following functions of simple random data:

1) p.random.rand(d0, d1, ..., dn)

This function of random module is used to generate random numbers or values in a given shape.

Example:

import numpy as np
a=np.random.rand(5,2)
a

Output:

array([[0.74710182, 0.13306399],
           [0.01463718, 0.47618842],
           [0.98980426, 0.48390004],
           [0.58661785, 0.62895758],
           [0.38432729, 0.90384119]])

2) np.random.randn(d0, d1, ..., dn)

This function of random module return a sample from the "standard normal" distribution.

Example:

import numpy as np
a=np.random.randn(2,2)
a

Output:

array([[ 1.43327469, -0.02019121],
       [ 1.54626422,  1.05831067]])
b=np.random.randn()
b
-0.3080190768904835

3) np.random.randint(low[, high, size, dtype])

This function of random module is used to generate random integers from inclusive(low) to exclusive(high).

Example:

import numpy as np
a=np.random.randint(3, size=10)
a

Output:

array([1, 1, 1, 2, 0, 0, 0, 0, 0, 0])

4) np.random.random_integers(low[, high, size])

This function of random module is used to generate random integers number of type np.int between low and high.

Example:

import numpy as np
a=np.random.random_integers(3)
a
b=type(np.random.random_integers(3))
b
c=np.random.random_integers(5, size=(3,2))
c

Output:

2
<type 'numpy.int32'>
array([[1, 1],
           [2, 5],
           [1, 3]])

5) np.random.random_sample([size])

This function of random module is used to generate random floats number in the half-open interval [0.0, 1.0).

Example:

import numpy as np
a=np.random.random_sample()
a
b=type(np.random.random_sample())
b
c=np.random.random_sample((5,))
c

Output:

0.09250360565571492
<type 'float'>
array([0.34665418, 0.47027209, 0.75944969, 0.37991244, 0.14159746])

6) np.random.random([size])

This function of random module is used to generate random floats number in the half-open interval [0.0, 1.0).

Example:

import numpy as np
a=np.random.random()
a
b=type(np.random.random())
b
c=np.random.random((5,))
c

Output:

0.008786953974334155
<type 'float'>
array([0.05530122, 0.59133394, 0.17258794, 0.6912388 , 0.33412534])

7) np.random.ranf([size])

This function of random module is used to generate random floats number in the half-open interval [0.0, 1.0).

Example:

import numpy as np
a=np.random.ranf()
a
b=type(np.random.ranf())
b
c=np.random.ranf((5,))
c

Output:

0.2907792098474542
<type 'float'>
array([0.34084881, 0.07268237, 0.38161256, 0.46494681, 0.88071377])

8) np.random.sample([size])

This function of random module is used to generate random floats number in the half-open interval [0.0, 1.0).

Example:

import numpy as np
a=np.random.sample()
a
b=type(np.random.sample())
b
c=np.random.sample((5,))
c

Output:

0.012298209913766511
<type 'float'>
array([0.71878544, 0.11486169, 0.38189074, 0.14303308, 0.07217287])

9) np.random.choice(a[, size, replace, p])

This function of random module is used to generate random sample from a given 1-D array.

Example:

import numpy as np
a=np.random.choice(5,3)
a
b=np.random.choice(5,3, p=[0.2, 0.1, 0.4, 0.2, 0.1])
b

Output:

array([0, 3, 4])
array([2, 2, 2], dtype=int64)

10) np.random.bytes(length)

This function of random module is used to generate random bytes.

Example:

import numpy as np
a=np.random.bytes(7)
a

Output:

'nQ\x08\x83\xf9\xde\x8a'

Permutations

There are the following functions of permutations:

1) np.random.shuffle()

This function is used for modifying a sequence in-place by shuffling its contents.

Example:

import numpy as np
a=np.arange(12)
a
np.random.shuffle(a)
a

Output:

array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11])
array([10,  3,  2,  4,  5,  8,  0,  9,  1, 11,  7,  6])

2) np.random.permutation()

This function permute a sequence randomly or return a permuted range.

Example:

import numpy as np
a=np.random.permutation(12)
a

Output:

array([ 8,  7,  3, 11,  6,  0,  9, 10,  2,  5,  4,  1])

Distributions

There are the following functions of permutations:

1) beta(a, b[, size])

This function is used to draw samples from a Beta distribution.

Example:

def setup(self):
        self.dist = dist.beta
        self.cargs = []
        self.ckwd = dict(alpha=2, beta=3)
        self.np_rand_fxn = numpy.random.beta
        self.np_args = [2, 3]
        self.np_kwds = dict()

2) binomial(n, p[, size])

This function is used to draw sample from a binomial distribution.

Example:

import numpy as np
n, p = 10, .6
s1= np.random.binomial(n, p, 10)
s1

Output:

array([6, 7, 7, 9, 3, 7, 8, 6, 6, 4])

3) chisquare(df[, size])

This function is used to draw sample from a binomial distribution.

Example:

import numpy as np
np.random.chisquare(2,4)
sum(np.random.binomial(9, 0.1, 20000) == 0)/20000.

Output:

array([6, 7, 7, 9, 3, 7, 8, 6, 6, 4])

4) dirichlet(alpha[, size])

This function is used to draw a sample from the Dirichlet distribution.

Example:

Import numpy as np
import matplotlib.pyplot as plt
s1 = np.random.dirichlet((10, 5, 3), 20).transpose()
plt.barh(range(20), s1[0])
plt.barh(range(20), s1[1], left=s1[0], color='g')
plt.barh(range(20), s1[2], left=s1[0]+s1[1], color='r')
plt.title("Lengths of Strings")
plt.show()

Output:

5) exponential([scale, size])

This function is used to draw sample from an exponential distribution.

Example:

def __init__(self, sourceid, targetid):
		self.__type = 'Transaction'
		self.id = uuid4()
		self.source = sourceid
		self.target = targetid
		self.date = self._datetime.date(start=2015, end=2019)
		self.time = self._datetime.time()

		if random() < 0.05:
			self.amount = self._numbers.between(100000, 1000000)
		self.amount = npr.exponential(10)

		if random() < 0.15:
			self.currency = self._business.currency_iso_code()
		else:
			self.currency = None

6) f(dfnum, dfden[, size])

This function is used to draw sample from an F distribution.

Example:

import numpy as np
dfno= 1.
dfden = 48.
s1 = np.random.f(dfno, dfden, 10)
np.sort(s1)

Output:

array([0.00264041, 0.04725478, 0.07140803, 0.19526217, 0.23979   ,
       0.24023478, 0.63141254, 0.95316446, 1.40281789, 1.68327507])

7) gamma(shape[, scale, size])

This function is used to draw sample from a Gamma distribution

Example:

import numpy as np
shape, scale = 2., 2.
s1 = np.random.gamma(shape, scale, 1000)
import matplotlib.pyplot as plt
import scipy.special as spss
count, bins, ignored = plt.hist(s1, 50, density=True)
a = bins**(shape-1)*(np.exp(-bins/scale) /
(spss.gamma(shape)*scale**shape))
plt.plot(bins, a, linewidth=2, color='r')
plt.show()

8) geometric(p[, size])

This function is used to draw sample from a geometric distribution.

Example:

import numpy as np
a = np.random.geometric(p=0.35, size=10000)
(a == 1).sum() / 1000

Output:

3.

9) gumbel([loc, scale, size])

This function is used to draw sample from a Gumble distribution.

Example:

import numpy as np
lov, scale = 0, 0.2
s1 = np.random.gumbel(loc, scale, 1000)
import matplotlib.pyplot as plt
count, bins, ignored = plt.hist(s1, 30, density=True)
plt.plot(bins, (1/beta)*np.exp(-(bins - loc)/beta)* np.exp( -np.exp( -(bins - loc) /beta) ),linewidth=2, color='r')
plt.show()

Output:

10) hypergeometric(ngood, nbad, nsample[, size])

This function is used to draw sample from a Hypergeometric distribution.

Example:

import numpy as np
good, bad, samp = 100, 2, 10
s1 = np.random.hypergeometric(good, bad, samp, 1000)
plt.hist(s1)
plt.show()

Output:

(array([ 13.,   0.,   0.,   0.,   0., 163.,   0.,   0.,   0., 824.]), array([ 8. ,  8.2,  8.4,  8.6,  8.8,  9. ,  9.2,  9.4,  9.6,  9.8, 10. ]), <a list of 10 Patch objects>)

numpy.random in Python

11) laplace([loc, scale, size])

This function is used to draw sample from the Laplace or double exponential distribution with specified location and scale.

Example:

import numpy as np
location, scale = 0., 2.
s = np.random.laplace(location, scale, 10)
s

Output:

array([-2.77127948, -1.46401453, -0.03723516, -1.61223942,  2.29590691,
        1.74297722,  1.49438411,  0.30325513, -0.15948891, -4.99669747])

12) logistic([loc, scale, size])

This function is used to draw sample from logistic distribution.

Example:

import numpy as np
import matplotlib.pyplot as plt
location, scale = 10, 1
s1 = np.random.logistic(location, scale, 10000)
count, bins, ignored = plt.hist(s1, bins=50)
count
bins
ignored
plt.show()

Output:

array([1.000e+00, 1.000e+00, 1.000e+00, 0.000e+00, 1.000e+00, 1.000e+00,
       1.000e+00, 5.000e+00, 7.000e+00, 1.100e+01, 1.800e+01, 3.500e+01,
       5.300e+01, 6.700e+01, 1.150e+02, 1.780e+02, 2.300e+02, 3.680e+02,
       4.910e+02, 6.400e+02, 8.250e+02, 9.100e+02, 9.750e+02, 1.039e+03,
       9.280e+02, 8.040e+02, 6.530e+02, 5.240e+02, 3.380e+02, 2.470e+02,
       1.650e+02, 1.150e+02, 8.500e+01, 6.400e+01, 3.300e+01, 1.600e+01,
       2.400e+01, 1.400e+01, 4.000e+00, 5.000e+00, 2.000e+00, 2.000e+00,
       1.000e+00, 1.000e+00, 0.000e+00, 1.000e+00, 0.000e+00, 0.000e+00,
       0.000e+00, 1.000e+00])
array([ 0.50643911,  0.91891814,  1.33139717,  1.7438762 ,  2.15635523,
        2.56883427,  2.9813133 ,  3.39379233,  3.80627136,  4.2187504 ,
        4.63122943,  5.04370846,  5.45618749,  5.86866652,  6.28114556,
        6.69362459,  7.10610362,  7.51858265,  7.93106169,  8.34354072,
        8.75601975,  9.16849878,  9.58097781,  9.99345685, 10.40593588,
       10.81841491, 11.23089394, 11.64337298, 12.05585201, 12.46833104,
       12.88081007, 13.2932891 , 13.70576814, 14.11824717, 14.5307262 ,
       14.94320523, 15.35568427, 15.7681633 , 16.18064233, 16.59312136,
       17.00560039, 17.41807943, 17.83055846, 18.24303749, 18.65551652,
       19.06799556, 19.48047459, 19.89295362, 20.30543265, 20.71791168,
       21.13039072])
<a list of 50 Patch objects>

numpy.random in Python

13) lognormal([mean, sigma, size])

This function is used to draw sample from a log-normal distribution.

Example:

import numpy as np
mu, sigma = 2., 1.
s1 = np.random.lognormal(mu, sigma, 1000)
import matplotlib.pyplot as plt
count, bins, ignored = plt.hist(s1, 100, density=True, align='mid')
a = np.linspace(min(bins), max(bins), 10000)
pdf = (np.exp(-(np.log(a) - mu)**2 / (2 * sigma**2))/ (a * sigma * np.sqrt(2 * np.pi)))
plt.plot(a, pdf, linewidth=2, color='r')
plt.axis('tight')
plt.show()

Output:

14) logseries(p[, size])

This function is used to draw sample from a logarithmic distribution.

Example:

import numpy as np
x = .6
s1 = np.random.logseries(x, 10000)
count, bins, ignored = plt.hist(s1)
def logseries(k, p):
return -p**k/(k*log(1-p))
plt.plot(bins, logseries(bins, x)*count.max()/logseries(bins, a).max(), 'r')
plt.show()

Output:

15) multinomial(n, pvals[, size])

This function is used to draw sample from a multinomial distribution.

Example:

import numpy as np
np.random.multinomial(20, [1/6.]*6, size=1)

Output:

array([[4, 2, 5, 5, 3, 1]])

16) multivariate_normal(mean, cov[, size, ...)

This function is used to draw sample from a multivariate normal distribution.

Example:

import numpy as np
mean = (1, 2)
coveriance = [[1, 0], [0, 100]] 
import matplotlib.pyplot as plt
a, b = np.random.multivariate_normal(mean, coveriance, 5000).T
plt.plot(a, b, 'x')
plt.axis('equal'023
030
)
plt.show()

Output:

17) negative_binomial(n, p[, size])

This function is used to draw sample from a negative binomial distribution.

Example:

import numpy as np
s1 = np.random.negative_binomial(1, 0.1, 100000)
for i in range(1, 11):
probability = sum(s1<i) / 100000.
print i, "wells drilled, probability of one success =", probability

Output:

1 wells drilled, probability of one success = 0
2 wells drilled, probability of one success = 0
3 wells drilled, probability of one success = 0
4 wells drilled, probability of one success = 0
5 wells drilled, probability of one success = 0
6 wells drilled, probability of one success = 0
7 wells drilled, probability of one success = 0
8 wells drilled, probability of one success = 0
9 wells drilled, probability of one success = 0
10 wells drilled, probability of one success = 0

18) noncentral_chisquare(df, nonc[, size])

This function is used to draw sample from a noncentral chi-square distribution.

Example:

import numpy as np
import matplotlib.pyplot as plt
val = plt.hist(np.random.noncentral_chisquare(3, 25, 100000), bins=200, normed=True)
plt.show()

Output:

19) normal([loc, scale, size])

This function is used to draw sample from a normal distribution.

Example:

import numpy as np
import matplotlib.pyplot as plt
mu, sigma = 0, 0.2 # mean and standard deviation
s1 = np.random.normal(mu, sigma, 1000)
abs(mu - np.mean(s1)) < 0.01
abs(sigma - np.std(s1, ddof=1)) < 0.01
count, bins, ignored = plt.hist(s1, 30, density=True)
plt.plot(bins, 1/(sigma * np.sqrt(2 * np.pi)) *np.exp( - (bins - mu)**2 / (2 * sigma**2) ), linewidth=2, color='r')
plt.show()

Output:

20) pareto(a[, size])

This function is used to draw samples from a Lomax or Pareto II with specified shape.

Example:

import numpy as np
import matplotlib.pyplot as plt
b, m1 = 3., 2.  # shape and mode
s1 = (np.random.pareto(b, 1000) + 1) * m1
count, bins, _ = plt.hist(s1, 100, density=True)
fit = b*m**b / bins**(b+1)
plt.plot(bins, max(count)*fit/max(fit), linewidth=2, color='r')
plt.show()

Output:

21) power(a[, size])

This function is used to draw samples in [0, 1] from a power distribution with positive exponent a-1.

Example:

import numpy as np
x = 5. # shape
samples = 1000
s1 = np.random.power(x, samples)
import matplotlib.pyplot as plt
count, bins, ignored = plt.hist(s1, bins=30)
a = np.linspace(0, 1, 100)
b = x*a**(x-1.)
density_b = samples*np.diff(bins)[0]*b
plt.plot(a, density_b)
plt.show()

Output:

22) rayleigh([scale, size])

This function is used to draw sample from a Rayleigh distribution.

Example:

val = hist(np.random.rayleigh(3, 100000), bins=200, density=True)
meanval = 1
modeval = np.sqrt(2 / np.pi) * meanval
s1 = np.random.rayleigh(modeval, 1000000)
100.*sum(s1>3)/1000000.

Output:

0.087300000000000003

numpy.random in Python

23) standard_cauchy([size])

This function is used to draw sample from a standard Cauchy distribution with mode=0.

Example:

import numpy as np
import matplotlib.pyplot as plt
s1 = np.random.standard_cauchy(1000000)
s1 = s1[(s1>-25) & (s1<25)]  # truncate distribution so it plots well
plt.hist(s1, bins=100)
plt.show()

Output:

24) standard_exponential([size])

This function is used to draw sample from a standard exponential distribution.

Example:

import numpy as np
n = np.random.standard_exponential((2, 7000))

Output:

array([[0.53857931, 0.181262  , 0.20478701, ..., 3.66232881, 1.83882709,
        1.77963295],
       [0.65163973, 1.40001955, 0.7525986 , ..., 0.76516523, 0.8400617 ,
        0.88551011]])

25) standard_gamma([size])

This function is used to draw sample from a standard Gamma distribution.

Example:

import numpy as np
shape, scale = 2., 1.
s1 = np.random.standard_gamma(shape, 1000000)
import matplotlib.pyplot as plt
import scipy.special as sps
count1, bins1, ignored1 = plt.hist(s, 50, density=True)
y = bins1**(shape-1) * ((np.exp(-bins1/scale))/ (sps.gamma(shape) * scale**shape))
plt.plot(bins1, y, linewidth=2, color='r')
plt.show()

Output:

26) standard_normal([size])

This function is used to draw sample from a standard Normal distribution.

Example:

import numpy as np
import matplotlib.pyplot as plt
s1= np.random.standard_normal(8000)
s1
q = np.random.standard_normal(size=(3, 4, 2))
q 

Output:

array([-3.14907597,  0.95366265, -1.20100026, ...,  3.47180222,
        0.9608679 ,  0.0774319 ])
array([[[ 1.55635461, -1.29541713],
        [-1.50534663, -0.02829194],
        [ 1.03949348, -0.26128132],
        [ 1.51921798,  0.82136178]],

       [[-0.4011052 , -0.52458858],
        [-1.31803814,  0.37415379],
        [-0.67077365,  0.97447018],
        [-0.20212115,  0.67840888]],

       [[ 1.86183474,  0.19946562],
        [-0.07376021,  0.84599701],
        [-0.84341386,  0.32081667],
        [-3.32016062, -1.19029818]]])

27) standard_t(df[, size])

This function is used to draw sample from a standard Student's distribution with df degree of freedom.

Example:

intake = np.array([5260., 5470, 5640, 6180, 6390, 6515, 6805, 7515,8230,8770])
s1 = np.random.standard_t(10, size=100000)
np.mean(intake)
intake.std(ddof=1)
t = (np.mean(intake)-7725)/(intake.std(ddof=1)/np.sqrt(len(intake)))
h = plt.hist(s1, bins=100, density=True)
np.sum(s1<t) / float(len(s1))
plt.show()

Output:

6677.5
1174.1101831694598
0.00864

numpy.random in Python

28) triangular(left, mode, right[, size])

This function is used to draw sample from a triangular distribution over the interval.

Example:

import numpy as np
import matplotlib.pyplot as plt
h = plt.hist(np.random.triangular(-4, 0, 8, 1000000), bins=300,density=True)
plt.show()

Output:

29) uniform([low, high, size])

This function is used to draw sample from a uniform distribution.

Example:

import numpy as np
import matplotlib.pyplot as plt
s1 = np.random.uniform(-1,0,1000)
np.all(s1 >= -1)
np.all(s1 < 0)
count, bins, ignored = plt.hist(s1, 15, density=True)
plt.plot(bins, np.ones_like(bins), linewidth=2, color='r')
plt.show()

Output:

30) vonmises(m1, m2[, size])

This function is used to draw sample from a von Mises distribution.

Example:

import numpy as np
import matplotlib.pyplot as plt
m1, m2 = 0.0, 4.0
s1 = np.random.vonmises(m1, m2, 1000)
from scipy.special import i0
plt.hist(s1, 50, density=True)
x = np.linspace(-np.pi, np.pi, num=51)
y = np.exp(m2*np.cos(x-m1))/(2*np.pi*i0(m2))
plt.plot(x, y, linewidth=2, color='r')
plt.show()

Output:

31) wald(mean, scale[, size])

This function is used to draw sample from a Wald, or inverse Gaussian distribution.

Example:

import numpy as np
import matplotlib.pyplot as plt
h = plt.hist(np.random.wald(3, 3, 100000), bins=250, density=True)
plt.show()

Output:

32) weibull(a[, size])

This function is used to draw sample from a Weibull distribution.

Example:

import numpy as np
import matplotlib.pyplot as plt
from scipy import special
x=2.0
s=np.random.weibull(x, 1000)
a = np.arange(1, 100.)/50.
def weib(x, n, a):
return (a/n)*(x/n)**np.exp(-(x/n)**a)
count, bins, ignored = plt.hist(np.random.weibull(5.,1000))
a= np.arange(1,100.)/50.
scale = count.max()/weib(x, 1., 5.).max()
scale = count.max()/weib(a, 1., 5.).max()
plt.plot(x, weib(x, 1., 5.)*scale)
plt.show()

Output:

33) zipf(a[, size])

This function is used to draw sample from a Zipf distribution.

Example:

import numpy as np
import matplotlib.pyplot as plt
from scipy import special
x=2.0
s=np.random.zipf(x, 1000)
count, bins, ignored = plt.hist(s[s<50], 50, density=True)
a = np.arange(1., 50.)
b= a**(-x) / special.zetac(x)
plt.plot(a, b/max(b), linewidth=2, color='r')
plt.show()

Output: