Statistics/Normal distribution
Statistics/Normal distribution is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
Normal (or Gaussian) distribution is a freqently used distribution in statistics. While most programming languages provide a uniformly distributed random number generator, one can derive normally distributed random numbers from a uniform generator.
- The task
- Take a uniform random number generator and create a large (you decide how large) set of numbers that follow a normal (Gaussian) distribution. Calculate the dataset's mean and stddev, and show the histogram here.
- Mention any native language support for the generation of normally distributed random numbers.
- Reference
- You may refer to code in Statistics/Basic if available.
PARI/GP
<lang parigp>rnormal()={ my(pr=32*ceil(default(realprecision)*log(10)/log(4294967296)),u1=random(2^pr)*1.>>pr,u2=random(2^pr)*1.>>pr); sqrt(-2*log(u1))*cos(2*Pi*u1) \\ Could easily be extended with a second normal at very little cost. }; mean(v)={
sum(i=1,#v,v[i])/#v
}; stdev(v,mu="")={
if(mu=="",mu=mean(v)); sqrt(sum(i=1,#v,(v[i]-mu)^2))/#v
}; histogram(v,bins=16,low=0,high=1)={
my(u=vector(bins),width=(high-low)/bins); for(i=1,#v,u[(v[i]-low)\width+1]++); u
}; show(n)={
my(v=vector(n,i,rnormal()),m=mean(v),s=stdev(v,m),h,sz=ceil(n/300));
h=histogram(v,,vecmin(v)-.1,vecmax(v)+.1);
for(i=1,#h,for(j=1,h[i]\sz,print1("#"));print());
}; show(10^4)</lang>