I think the docstring of np.random.pareto (Version 1.8.0) is erroneous. In a nutshell np.random.pareto draws samples from a Lomax distribution with shape a and location m'=1. To convert those samples to a classical Pareto distribution with shape a and location m you have to add 1 and multiply by m, instead of adding m as stated in the docstring.
More specifically, the docstring says: "The Lomax or Pareto II distribution is a shifted Pareto distribution. The classical Pareto distribution can be obtained from the Lomax distribution by adding the location parameter m, see below." Instead, it should read "[..] by adding 1 and multiplying my m, see below." The example at the bottom therefore should read: >>> a, m = 3., 1. # shape and mode >>> s = (np.random.pareto(a, 1000) + 1) * m Maybe an example with m=10 makes it clearer >>> a, m = 3., 10. # shape and mode >>> s = (np.random.pareto(a, 1000) + 1) * m Additionally, calling m the location parameter could be misleading. For simple Pareto (Type I) distributions it is usually referred to as the x_min oder mode parameter of the distribution. When discussing generalized Pareto distributions m is usually called the scale parameter (a constant factor) while mu is the location (an additive term) [1]. I assume the misleading naming could have caused some confusion and lead to the errors described above. Last but not least I think it might also cause confusion to call a function 'pareto' while its meaning is 'shifted by -1 pareto'. :) [1] http://en.wikipedia.org/wiki/Generalized_Pareto_distribution -- Conny Kuehne _______________________________________________ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
