numpy.random.logistic — NumPy v1.11 Manual (original) (raw)

numpy.random.logistic(loc=0.0, scale=1.0, size=None)¶

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 : int or tuple of ints, optional Output shape. If the given shape is, e.g., (m, n, k), thenm * n * k samples are drawn. Default is None, in which case a single value is returned.
Returns:	samples : ndarray or scalar where the values are all integers in [0, n].

See also

scipy.stats.distributions.logistic

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

Notes

The probability density for the Logistic distribution is

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

where $\mu$ = 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.

References

[R232]	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.

[R233]	Weisstein, Eric W. “Logistic Distribution.” From MathWorld–A Wolfram Web Resource.http://mathworld.wolfram.com/LogisticDistribution.html

[R234]	Wikipedia, “Logistic-distribution”,http://en.wikipedia.org/wiki/Logistic_distribution

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()