papyri
{ } Raw JSON

bundles / numpy 2.4.4 / numpy / random / RandomState / lognormal

cython_function_or_method

numpy.random:RandomState.lognormal

Signature

def   lognormal ( mean = 0.0 ,  sigma = 1.0 ,  size = None )

Summary

Draw samples from a log-normal distribution.

Extended Summary

Draw samples from a log-normal distribution with specified mean, standard deviation, and array shape. Note that the mean and standard deviation are not the values for the distribution itself, but of the underlying normal distribution it is derived from.

Parameters

mean : float or array_like of floats, optional

Mean value of the underlying normal distribution. Default is 0.

sigma : float or array_like of floats, optional

Standard deviation of the underlying normal distribution. Must be non-negative. Default is 1.

size : int or tuple of ints, optional

Output shape. If the given shape is, e.g., (m, n, k), then m * n * k samples are drawn. If size is None (default), a single value is returned if mean and sigma are both scalars. Otherwise, np.broadcast(mean, sigma).size samples are drawn.

Returns

out : ndarray or scalar

Drawn samples from the parameterized log-normal distribution.

Notes

A variable x has a log-normal distribution if log(x) is normally distributed. The probability density function for the log-normal distribution is:

where is the mean and is the standard deviation of the normally distributed logarithm of the variable. A log-normal distribution results if a random variable is the product of a large number of independent, identically-distributed variables in the same way that a normal distribution results if the variable is the sum of a large number of independent, identically-distributed variables.

Examples

Draw samples from the distribution: 
mu, sigma = 3., 1. # mean and standard deviation
s = np.random.lognormal(mu, sigma, 1000)
✓
Display the histogram of the samples, along with the probability density function: 
import matplotlib.pyplot as plt
count, bins, ignored = plt.hist(s, 100, density=True, align='mid')
✓
x = np.linspace(min(bins), max(bins), 10000)
pdf = (np.exp(-(np.log(x) - mu)**2 / (2 * sigma**2))
       / (x * sigma * np.sqrt(2 * np.pi)))
✓
plt.plot(x, pdf, linewidth=2, color='r')
plt.axis('tight')
✗
plt.show()
✓
fig-bcb658a9024bf21d.png
Demonstrate that taking the products of random samples from a uniform distribution can be fit well by a log-normal probability density function. 
b = []
for i in range(1000):
   a = 10. + np.random.standard_normal(100)
   b.append(np.prod(a))
✓
b = np.array(b) / np.min(b) # scale values to be positive
count, bins, ignored = plt.hist(b, 100, density=True, align='mid')
sigma = np.std(np.log(b))
mu = np.mean(np.log(b))
✓
x = np.linspace(min(bins), max(bins), 10000)
pdf = (np.exp(-(np.log(x) - mu)**2 / (2 * sigma**2))
       / (x * sigma * np.sqrt(2 * np.pi)))
✓
plt.plot(x, pdf, color='r', linewidth=2)
✗
plt.show()
✓
fig-a74b7ebed9bb91b2.png

See also

random.Generator.lognormal

which should be used for new code.

scipy.stats.lognorm

probability density function, distribution, cumulative density function, etc.

Aliases

  • numpy.random.lognormal
  • numpy.random.RandomState.lognormal