# numpy.random.logistic

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).

  Note

  New code should use the `logistic` method of a `Generator` instance instead; please see the Quick Start.

  Parameters:
    loc float or array_like of floats, optional

      Parameter of the distribution. Default is 0.

    scale float or array_like of floats, optional

      Parameter of the distribution. Must be non-negative. Default is 1.

    size int 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:
    out ndarray or scalar

      Drawn samples from the parameterized logistic distribution.

  See also

  `scipy.stats.logistic`

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

  `random.Generator.logistic`

    which should be used for new code.

  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

  [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()