Re: Extended Random Function

*To*: mathgroup at smc.vnet.net*Subject*: [mg21782] Re: Extended Random Function*From*: Paul Abbott <paul at physics.uwa.edu.au>*Date*: Thu, 27 Jan 2000 22:57:05 -0500 (EST)*Organization*: University of Western Australia*References*: <85mk1o$1ag@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Daniele wrote: > I have a question concerning the use of the > extension of the Random[] function as defined in > the Statistics`ContinuousDistributions`. With > this extension it is possible to pick a random > number according to a given distribution function. > > My question is: how is it possible to pick a Real > number with n digits? With the default function > it is possible to do so by calling > > Random[Real,{xmin,xmax},ndigits] If you look through the code in Statistics`ContinuousDistributions` or Statistics`NormalDistribution` you will see that machine-precision is used. E.g., normal = Compile[{{mu, _Real}, {sigma, _Real}, {q1, _Real}, {q2, _Real}}, mu + sigma Sqrt[-2 Log[q1]] Cos[2Pi q2] ] NormalDistribution/: Random[NormalDistribution[mu_:0, sigma_:1]] := normal[mu, sigma, Random[], Random[]] and there is no option for specifying n digits. Note also that Compile requires the use of machine-precision. You could modify such functions as follows: normal = Function[{mu, sigma, q1, q2}, mu + sigma Sqrt[-2 Log[q1]] Cos[2Pi q2]]; replacing Compile with Function and removing the "argument typing", NormalDistribution/: Random[NormalDistribution[mu_:0, sigma_:1], ndigits_] := normal[mu, sigma, Random[Real, {0, 1}, ndigits], Random[Real, {0, 1}, ndigits]] adding an extra argument to NormalDistribution and modifying the calls to Random. For example, In[1]:= Random[NormalDistribution[1, 2], 25] Out[1]= 0.23230352490529443816318603637908270412 Cheers, Paul