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.
- Parameters
- locfloat or array_like of floats, optional
Parameter of the distribution. Default is 0.
- scalefloat or array_like of floats, optional
Parameter of the distribution. Must be non-negative.
Default is 1.
- sizeint 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
- outndarray or scalar
Drawn samples from the parameterized logistic distribution.
Notes
The probability density for the Logistic distribution is
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= location and
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= 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.
References
- 1
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.
- 2
Weisstein, Eric W. “Logistic Distribution.” From
MathWorld–A Wolfram Web Resource.
http://mathworld.wolfram.com/LogisticDistribution.html
- 3
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()