Statistics/Normal distribution: Difference between revisions
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=={{header|Liberty BASIC}}== |
=={{header|Liberty BASIC}}== |
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Uses LB Statistics/Basic |
Uses LB Statistics/Basic |
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<lang lb> |
<lang lb>call sample 100000 |
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call sample 100000 |
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end |
end |
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v =rnd( 1) |
v =rnd( 1) |
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normalDist =( -2 *log( u))^0.5 *cos( 2 *3.14159265 *v) |
normalDist =( -2 *log( u))^0.5 *cos( 2 *3.14159265 *v) |
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end function |
end function</lang> |
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</lang> |
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100000 data terms used. |
100000 data terms used. |
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Largest term was 4.12950792 & smallest was -4.37934139 |
Largest term was 4.12950792 & smallest was -4.37934139 |
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=={{header|PARI/GP}}== |
=={{header|PARI/GP}}== |
Revision as of 11:09, 19 October 2011
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.
Liberty BASIC
Uses LB Statistics/Basic <lang lb>call sample 100000
end
sub sample n
dim dat( n) for i =1 to n dat( i) =normalDist( 1, 0.2) next i
'// show mean, standard deviation. Find max, min. mx =-1000 mn = 1000 sum =0 sSq =0 for i =1 to n d =dat( i) mx =max( mx, d) mn =min( mn, d) sum =sum +d sSq =sSq +d^2 next i print n; " data terms used."
mean =sum / n print "Largest term was "; mx; " & smallest was "; mn range =mx -mn print "Mean ="; mean
print "Stddev ="; ( sSq /n -mean^2)^0.5
'// show histogram nBins =50 dim bins( nBins) for i =1 to n z =int( ( dat( i) -mn) /range *nBins) bins( z) =bins( z) +1 next i for b =0 to nBins -1 for j =1 to int( nBins *bins( b)) /n *30) print "#"; next j print next b print
end sub
function normalDist( m, s) ' Box Muller method
u =rnd( 1) v =rnd( 1) normalDist =( -2 *log( u))^0.5 *cos( 2 *3.14159265 *v)
end function</lang>
100000 data terms used. Largest term was 4.12950792 & smallest was -4.37934139 Mean =-0.26785425e-2 Stddev =1.00097669
# ## ### ##### ######## ############ ################ ######################## ############################## ###################################### ############################################## ######################################################## ################################################################### ############################################################################## ####################################################################################### ################################################################################################ #################################################################################################### ######################################################################################################## ##################################################################################################### ############################################################################################## ######################################################################################### ################################################################################## ######################################################################### ############################################################## #################################################### ########################################## ################################# ########################## ################## ############# ######### ###### #### ## # #
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>