numpy.random.
logistic
Draw samples from a logistic distribution.
Samples are drawn from a logistic distribution with specified parameters, loc (location or mean, also median), and scale (>0).
Note
New code should use the logistic method of a default_rng() instance instead; see random-quick-start.
default_rng()
Parameter of the distribution. Default is 0.
Parameter of the distribution. Must be non-negative. Default is 1.
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.
(m, n, k)
m * n * k
None
loc
scale
np.broadcast(loc, scale).size
Drawn samples from the parameterized logistic distribution.
See also
scipy.stats.logistic
probability density function, distribution or cumulative density function, etc.
Generator.logistic
which should be used for new code.
Notes
The probability density for the Logistic distribution is
System Message: WARNING/2 (P(x) = P(x) = \frac{e^{-(x-\mu)/s}}{s(1+e^{-(x-\mu)/s})^2}, )
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where
System Message: WARNING/2 (\mu)
System Message: WARNING/2 (s)
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.
References
Reiss, R.-D. and Thomas M. (2001), “Statistical Analysis of Extreme Values, from Insurance, Finance, Hydrology and Other Fields,” Birkhauser Verlag, Basel, pp 132-133.
Weisstein, Eric W. “Logistic Distribution.” From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/LogisticDistribution.html
Wikipedia, “Logistic-distribution”, https://en.wikipedia.org/wiki/Logistic_distribution
Examples
Draw samples from the distribution:
>>> loc, scale = 10, 1 >>> s = np.random.logistic(loc, scale, 10000) >>> import matplotlib.pyplot as plt >>> count, bins, ignored = plt.hist(s, bins=50)
# plot against distribution
>>> def logist(x, loc, scale): ... return np.exp((loc-x)/scale)/(scale*(1+np.exp((loc-x)/scale))**2) >>> lgst_val = logist(bins, loc, scale) >>> plt.plot(bins, lgst_val * count.max() / lgst_val.max()) >>> plt.show()
