Statistics/Normal distribution: Difference between revisions

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=={{header|Phix}}==

<lang Phix>~~procedure sample~~(~~integer n~~)

with javascript_semantics

-- show mean, standard deviation. Find max, min.

procedure sample(integer n)

sequence dat = repeat(0,n)

-- show mean, standard deviation. Find max, min.

for i=1 to n do

sequence dat = repeat(0,n)

dat[i] = sqrt(-2*log(rnd()))*cos(2*PI*rnd())

for i=1 to n do

end for

dat[i] = sqrt(-2*log(rnd()))*cos(2*PI*rnd())

printf(1,"%d data terms used.\n",{n})

end for

printf(1,"%d data terms used.\n",{n})

atom mean = sum(dat)/n,

mx = max(dat),

atom mean = sum(dat)/n,

mn = min(dat),

mx = max(dat),

range = mx-mn

mn = min(dat),

printf(1,"Largest term was %g & smallest was %g\n",{mx,mn})

range = mx-mn

printf(1,"Mean = %g\n",{mean})

printf(1,"Largest term was %g & smallest was %g\n",{mx,mn})

printf(1,"Stddev = %g\n",sqrt(sum(sq_mul(dat,dat))/n-mean*mean))

printf(1,"Mean = %g\n",{mean})

printf(1,"Stddev = %g\n",sqrt(sum(sq_mul(dat,dat))/n-mean*mean))

-- show histogram

integer nBins = 50

-- show histogram

sequence bins = repeat(0,nBins+1)

integer nBins = 50

for i=1 to n do

sequence bins = repeat(0,nBins+1)

bins[floor((dat[i]-mn)/range*nBins)+1] += 1

for i=1 to n do

end for

integer bdx = floor((dat[i]-mn)/range*nBins)+1

for b=1 to nBins do

bins[bdx] += 1

puts(1,repeat('#',floor(nBins*bins[b]/n*30))&"\n")

end for

end for

for b=1 to nBins do

end procedure

puts(1,repeat('#',floor(nBins*bins[b]/n*30))&"\n")

end for

sample(100000)</lang>

end procedure

sample(100000)

<pre>

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<lang Phix>~~function gaussian~~(~~atom mean, atom variance~~)

with javascript_semantics

return sqrt(-2 * variance * log(rnd())) *

function gaussian(atom mean, atom variance)

cos(2 * variance * PI * rnd()) + mean

return sqrt(-2 * variance * log(rnd())) *

end function

cos(2 * variance * PI * rnd()) + mean

end function

function mean(sequence t)

return sum(t)/length(t)

end function

function std(sequence t)

atom squares = 0,

avg = mean(t)

for i=1 to length(t) do

squares += power(avg-t[i],2)

end for

atom variance = squares/length(t)

return sqrt(variance)

end function

procedure showHistogram(sequence t)

for i=ceil(min(t)) to floor(max(t)) do

integer n = 0

for k=1 to length(t) do

n += ceil(t[k]-0.5)=i

end for

integer l = floor(n/length(t)*200)

printf(1,"%d %s %d\n",{i,repeat('=',l),n})

end for

end procedure

function mean(sequence t)

sequence t = repeat(0,100000)

return sum(t)/length(t)

integer avg = 50, variance = 10

end function

for i=1 to length(t) do

t[i] = gaussian(avg, variance)

function std(sequence t)

end for

atom squares = 0,

printf(1,"Mean: %g, expected %g\n",{mean(t),avg})

avg = mean(t)

printf(1,"StdDev: %g, expected %g\n",{std(t),sqrt(variance)})

for i=1 to length(t) do

showHistogram(t)</lang>

squares += power(avg-t[i],2)

end for

atom variance = squares/length(t)

return sqrt(variance)

end function

procedure showHistogram(sequence t)

for i=ceil(min(t)) to floor(max(t)) do

integer n = 0

for k=1 to length(t) do

n += ceil(t[k]-0.5)=i

end for

integer l = floor(n/length(t)*200)

printf(1,"%d %s %d\n",{i,repeat('=',l),n})

end for

end procedure

sequence t = repeat(0,100000)

integer avg = 50, variance = 10

for i=1 to length(t) do

t[i] = gaussian(avg, variance)

end for

printf(1,"Mean: %g, expected %g\n",{mean(t),avg})

printf(1,"StdDev: %g, expected %g\n",{std(t),sqrt(variance)})

showHistogram(t)

<pre>