RandomArbitraryPdf

class marxs.math.random.RandomArbitraryPdf(x, pdf, randomize_in_bin=True, sort=True)

Bases: object

Take random draw from an arbitrary (and arbitrarily binned) pdf.

The PDF is approximated as piecewice constant. The object is initialized with a parameters that describe the PDF, the object can then be called with the number of random samples that are required.

Parameters:

xnp.array

Upper bin edge for input bins

pdfnp.array

Value of the pdf for each bin. pdf[0] is ignored, since the lower edge of that bin is undefined.

randomize_in_binbool

If True randomize the return value over each bin. If False the return value will be exactly the upper bin edge.

sortbool

When calculating the cdf from a pdf that covers a large dynamical range, round-off errors may occur. If True this sorts the input bins in size (keeping an index for reverse the operation later) to avoid numerical errors.

References

https://en.wikipedia.org/wiki/Pseudorandom_number_generator#Non-uniform_generators

http://stackoverflow.com/questions/21100716/

Examples

First, and example with two bins (1-2 and 2-3). The probability density for each bin is 1 and 6, respectively (the 0.2 is ignored, because the range XXX - 1 is not a valid bin since the lower bound is undefined).

>>> import numpy as np
>>> # Set seed so this example returns exact same numbers every time
>>> np.random.seed(0)
>>> a = RandomArbitraryPdf(np.array([1,2,3]), np.array([0.2,1,6]))
>>> a(10)
array([2.79172504, 2.52889492, 2.56804456, 2.92559664, 2.07103606,
       2.0871293 , 2.0202184 , 2.83261985, 2.77815675, 2.87001215])

As you can see, in this case the chance to draw from the 1-2 interval is only 1/7 and it did not happen this time.

If, instead, we want to have exact (upper) bin edges returned it looks like this: >>> a = RandomArbitraryPdf(np.array([1,2,3]), np.array([0,1,6]), randomize_in_bin=False) >>> a(10) array([3, 3, 3, 3, 2, 3, 3, 3, 3, 3])

As expected, most numbers are 3, with a 2 mixed in.

Methods Summary

__call__(N)

Draw from the distribution function.

Methods Documentation

__call__(N)

Draw from the distribution function. See docstring of class.