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# numpy.random.logistic

`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 : {tuple, int} Output shape. If the given shape is, e.g., `(m, n, k)`, then `m * n * k` samples are drawn.
  Returns: | samples : {ndarray, 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

  where = location and = 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

  [73] | 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.

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

  [75] | 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()

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