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Diffstat (limited to 'Doc/library')
| -rw-r--r-- | Doc/library/random.rst | 68 |
1 files changed, 37 insertions, 31 deletions
diff --git a/Doc/library/random.rst b/Doc/library/random.rst index c43307c..d37fd9c 100644 --- a/Doc/library/random.rst +++ b/Doc/library/random.rst @@ -253,6 +253,8 @@ Functions for sequences order so that the sample is reproducible. +.. _real-valued-distributions: + Real-valued distributions ------------------------- @@ -516,26 +518,42 @@ Simulation of arrival times and service deliveries for a multiserver queue:: print(f'Mean wait: {mean(waits):.1f}. Stdev wait: {stdev(waits):.1f}.') print(f'Median wait: {median(waits):.1f}. Max wait: {max(waits):.1f}.') +.. seealso:: + + `Statistics for Hackers <https://www.youtube.com/watch?v=Iq9DzN6mvYA>`_ + a video tutorial by + `Jake Vanderplas <https://us.pycon.org/2016/speaker/profile/295/>`_ + on statistical analysis using just a few fundamental concepts + including simulation, sampling, shuffling, and cross-validation. + + `Economics Simulation + <http://nbviewer.jupyter.org/url/norvig.com/ipython/Economics.ipynb>`_ + a simulation of a marketplace by + `Peter Norvig <http://norvig.com/bio.html>`_ that shows effective + use of many of the tools and distributions provided by this module + (gauss, uniform, sample, betavariate, choice, triangular, and randrange). + + `A Concrete Introduction to Probability (using Python) + <http://nbviewer.jupyter.org/url/norvig.com/ipython/Probability.ipynb>`_ + a tutorial by `Peter Norvig <http://norvig.com/bio.html>`_ covering + the basics of probability theory, how to write simulations, and + how to perform data analysis using Python. + + Recipes ------- The default :func:`.random` returns multiples of 2⁻⁵³ in the range -*0.0 ≤ x < 1.0*. All such numbers are evenly spaced and exactly +*0.0 ≤ x < 1.0*. All such numbers are evenly spaced and are exactly representable as Python floats. However, many floats in that interval are not possible selections. For example, ``0.05954861408025609`` isn't an integer multiple of 2⁻⁵³. The following recipe takes a different approach. All floats in the -interval are possible selections. Conceptually it works by choosing -from evenly spaced multiples of 2⁻¹⁰⁷⁴ and then rounding down to the -nearest representable float. - -For efficiency, the actual mechanics involve calling -:func:`~math.ldexp` to construct a representable float. The mantissa -comes from a uniform distribution of integers in the range *2⁵² ≤ -mantissa < 2⁵³*. The exponent comes from a geometric distribution -where exponents smaller than *-53* occur half as often as the next -larger exponent. +interval are possible selections. The mantissa comes from a uniform +distribution of integers in the range *2⁵² ≤ mantissa < 2⁵³*. The +exponent comes from a geometric distribution where exponents smaller +than *-53* occur half as often as the next larger exponent. :: @@ -553,7 +571,8 @@ larger exponent. exponent += x.bit_length() - 32 return ldexp(mantissa, exponent) -All of the real valued distributions will use the new method:: +All :ref:`real valued distributions <real-valued-distributions>` +in the class will use the new method:: >>> fr = FullRandom() >>> fr.random() @@ -561,27 +580,14 @@ All of the real valued distributions will use the new method:: >>> fr.expovariate(0.25) 8.87925541791544 +The recipe is conceptually equivalent to an algorithm that chooses from +all the multiples of 2⁻¹⁰⁷⁴ in the range *0.0 ≤ x < 1.0*. All such +numbers are evenly spaced, but most have to be rounded down to the +nearest representable Python float. (The value 2⁻¹⁰⁷⁴ is the smallest +positive unnormalized float and is equal to ``math.ulp(0.0)``.) -.. seealso:: - - `Statistics for Hackers <https://www.youtube.com/watch?v=Iq9DzN6mvYA>`_ - a video tutorial by - `Jake Vanderplas <https://us.pycon.org/2016/speaker/profile/295/>`_ - on statistical analysis using just a few fundamental concepts - including simulation, sampling, shuffling, and cross-validation. - - `Economics Simulation - <http://nbviewer.jupyter.org/url/norvig.com/ipython/Economics.ipynb>`_ - a simulation of a marketplace by - `Peter Norvig <http://norvig.com/bio.html>`_ that shows effective - use of many of the tools and distributions provided by this module - (gauss, uniform, sample, betavariate, choice, triangular, and randrange). - `A Concrete Introduction to Probability (using Python) - <http://nbviewer.jupyter.org/url/norvig.com/ipython/Probability.ipynb>`_ - a tutorial by `Peter Norvig <http://norvig.com/bio.html>`_ covering - the basics of probability theory, how to write simulations, and - how to perform data analysis using Python. +.. seealso:: `Generating Pseudo-random Floating-Point Values <https://allendowney.com/research/rand/downey07randfloat.pdf>`_ a |