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).
Parameters: | loc : float
scale : float > 0.
size : {tuple, int}
Output shape. If the given shape is, e.g., (m, n, k), then
m * n * k samples are drawn.
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Returns: | samples : {ndarray, scalar}
where the values are all integers in [0, n].
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See also
- scipy.stats.distributions.logistic
- probability density function, distribution or cumulative density function, etc.
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
[R203] | 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. |
Examples
Draw samples from the distribution:
>>> loc, scale = 10, 1
>>> s = np.random.logistic(loc, scale, 10000)
>>> count, bins, ignored = plt.hist(s, bins=50)
# plot against distribution
>>> def logist(x, loc, scale):
... return exp((loc-x)/scale)/(scale*(1+exp((loc-x)/scale))**2)
>>> plt.plot(bins, logist(bins, loc, scale)*count.max()/\
... logist(bins, loc, scale).max())
>>> plt.show()