# -*- org -*-

#+CATEGORY: randist

*   ACM Computing Surveys (CSUR)  

   Volume 39 ,  Issue 4  (2007)                                                                     

   Gaussian random number generators                                                                

   David B. Thomas, Wayne Luk, Philip H.W. Leong, John D. Villasenor                                

   Article No. 11                                                                                   

* add Erlang dist back in?

* DONE, for mu. 

  Note that we need to get rid of mu when it is not the mean.

  From: Brian Gough <bjg@network-theory.co.uk>

  To: briggsk@info.bt.co.uk

  Cc: gsl-discuss@sourceware.cygnus.com

  Subject: Re: Pareto Distribution

  Date: Sun, 9 Jul 2000 20:05:03 +0100 (BST)

  Yes, we should adopt the conventions from a standard reference book --

  the existing functions are drawn from a variety of sources, mostly

  Devroye's book on Random Variates (which is public domain, but not

  available electronically unfortunately).  Maybe the three volumes of

  Johnson & Kotz on Univariate Distributions would do, for

  example. Patches are welcome from anyone who wants sort this out.

  Keith Briggs writes:

   > Another thing to think about: some of the other distributions

   > have a argument `mu' to the C function which is a parameter

   > which is not the mean.   This is non-standard and confusing.

   > (Also, in the Pareto function, `a' is normally called beta,

   > `b' is normally called alpha.)

   > 

   > Keith

   > 

   > +-------------------------------------------------------------------+

   > | Dr. Keith M. Briggs, Complexity Research Group, BT Research Labs. |

   > | Adastral Park admin2 pp5, Martlesham Heath, IP5 3RE, Suffolk,  UK |

   > | Tel. 01473 641 911  Fax. 01473 647 410.  Home tel:  01473 625 972 |

   > | www.bt.com | personal homepage:  www.labs.bt.com/people/briggsk2/ |

   > +-------------------------------------------------------------------+

* The exponential power distribution method could be speeded up by

using a rational function approximation for the rejection scaling

parameter.

* Do something about the possibility of the user providing invalid

parameters (e.g. negative variance etc). Not sure what to do though,

since returning an error code is not possible. Maybe just return zero.

  We should return NAN in this case, and for the CDFs.

* Add the triangular distribution.

* Look at Marsaglia & Tsang, "The Monte Python Method for generating

random variables", ACM TOMS Vol 24, No 3, p341 

and the paper on the Ziggurat Method: Journal of Statistical Software,

Volume 05 Issue 08. George Marsaglia and Wai Wan Tsang. "The ziggurat

method for generating random variables"

* Should 0 be included in distributions such as the exponential

distribution? If we want a consistent behaviour, is it included in

others?  Note that 1-gsl_rng_uniform() can have a slight loss of

precision when the random float is small.