`numpy.random._generator:Generator.logistic`

Signature

def logistic ( loc = 0.0 , scale = 1.0 , size = None )

Summary

Draw samples from a logistic distribution.

Extended Summary

Samples are drawn from a logistic distribution with specified parameters, loc (location or mean, also median), and scale (>0).

Parameters

loc : float or array_like of floats, optional: Parameter of the distribution. Default is 0.
scale : float or array_like of floats, optional: Parameter of the 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 loc and scale are both scalars. Otherwise, np.broadcast(loc, scale).size samples are drawn.

Returns

out : ndarray or scalar: Drawn samples from the parameterized logistic distribution.

Notes

The probability density for the Logistic distribution is

P (x) = \frac{e ^{- (x - μ) / s}}{s ( 1 + e ^{- (x - μ) / s} ) ^{2}},

where $μ$ = location and $s$ = scale.

The Logistic distribution is used in Extreme Value problems where it can act as a mixture of Gumbel distributions, in Epidemiology, and by the World Chess Federation (FIDE) where it is used in the Elo ranking system, assuming the performance of each player is a logistically distributed random variable.

Examples

Draw samples from the distribution:

loc, scale = 10, 1
rng = np.random.default_rng()
s = rng.logistic(loc, scale, 10000)
import matplotlib.pyplot as plt
count, bins, _ = plt.hist(s, bins=50, label='Sampled data')

✓

# plot sampled data against the exact distribution

def logistic(x, loc, scale):
    return np.exp((loc-x)/scale)/(scale*(1+np.exp((loc-x)/scale))**2)
logistic_values  = logistic(bins, loc, scale)
bin_spacing = np.mean(np.diff(bins))

✓

plt.plot(bins, logistic_values  * bin_spacing * s.size, label='Logistic PDF')
plt.legend()

✗

plt.show()

✓

Aliases

numpy.random.Generator.logistic