Statistics/Normal distribution: Difference between revisions
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m (→{{header|REXX}}: changed whitespace in the output section. used a template for the output.) |
m (→{{header|REXX}}: changed comments and whitespace, optimized some computations.) |
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if datatype(seed,'W') then call random ,,seed /*seed is for repeatable RANDOM numbers*/ |
if datatype(seed,'W') then call random ,,seed /*seed is for repeatable RANDOM numbers*/ |
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call pi /*call subroutine to define pi constant*/ |
call pi /*call subroutine to define pi constant*/ |
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do g=1 for n |
do g=1 for n; #.g= sqrt( -2 * ln( rand() ) ) * cos( 2 * pi * rand() ) |
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end /*g*/ /* [↑] uniform random number ───► #.g */ |
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s=0 |
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end /*g*/ |
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ss=0 |
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| ⚫ | |||
do j=1 for n; _=#.j; s=s+_; ss=ss+_*_ /*the sum, and the sum of squares. */ |
do j=1 for n; _=#.j; s=s+_; ss=ss+_*_ /*the sum, and the sum of squares. */ |
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mn=min(mn, |
mn=min(mn, _); mx=max(mx, _) /*find the minimum and the maximum. */ |
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end /*j*/ |
end /*j*/ |
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!.=0 |
!.=0 |
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say ' maximum = ' aa(mx ) |
say ' maximum = ' aa(mx ) |
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say ' arithmetic mean = ' aa(s/n) |
say ' arithmetic mean = ' aa(s/n) |
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say ' standard deviation = ' aa(sqrt(ss/n - (s/n)**2) ) |
say ' standard deviation = ' aa(sqrt( ss/n - (s/n) **2) ) |
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?mn=!.1; ?mx=?mn /*define minimum & maximum value so far*/ |
?mn=!.1; ?mx=?mn /*define minimum & maximum value so far*/ |
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parse value scrSize() with sd sw . /*obtain the (true) screen size of term*/ /*◄──not all REXXes have this BIF*/ |
parse value scrSize() with sd sw . /*obtain the (true) screen size of term*/ /*◄──not all REXXes have this BIF*/ |
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sdE=sd- |
sdE= sd - 4 /*the effective (useable) screen depth.*/ |
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swE=sw- |
swE= sw - 1 /* " " " " width.*/ |
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$=1 / max(1,mx-mn) * sdE |
$=1 / max(1, mx-mn) * sdE /*$ is used for scaling depth of histo*/ |
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do i=1 for n; ?=trunc((#.i-mn) * $) |
do i=1 for n; ?=trunc( (#.i-mn) * $) /*calculate the relative line.*/ |
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!.?=!.?+ |
!.?= !.? + 1 /*bump the counter. */ |
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?mn=min(?mn, !.?); ?mx=max(?mx, !.?) /*find the minimum and maximum*/ |
?mn=min(?mn, !.?); ?mx=max(?mx, !.?) /*find the minimum and maximum*/ |
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end /*i*/ |
end /*i*/ |
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f=swE/?mx /*limit graph to 1 full screen*/ |
f=swE/?mx /*limit graph to 1 full screen*/ |
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do h=0 for sdE; _=!.h /*obtain a data point. */ |
do h=0 for sdE; _=!.h /*obtain a data point. */ |
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if _>noise then say copies('─', trunc(_*f |
if _>noise then say copies('─', trunc(_*f) ) /*display a bar of histogram. */ |
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end /*h*/ /*[↑] use a hyphen for histo.*/ |
end /*h*/ /*[↑] use a hyphen for histo.*/ |
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exit /*stick a fork in it, we're all done. */ |
exit /*stick a fork in it, we're all done. */ |
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/*──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────*/ |
/*──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────*/ |
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aa: parse arg a; return left('',(a>=0)+2*datatype(a,'W'))a |
aa: parse arg a; return left('', (a>=0) + 2 * datatype(a, 'W'))a /*prepend a blank if #>=0, add 2 blanks if whole.*/ |
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e: e =2.7182818284590452353602874713526624977572470936999595749669676277240766303535; return e |
e: e =2.7182818284590452353602874713526624977572470936999595749669676277240766303535; return e |
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pi: pi=3.1415926535897932384626433832795028841971693993751058209749445923078164062862; return pi |
pi: pi=3.1415926535897932384626433832795028841971693993751058209749445923078164062862; return pi |
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r2r: return arg(1) // (pi() * 2) /*normalize the given angle (in radians) to ±2pi.*/ |
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rand: return random(1, 1e5) / 1e5 /*REXX generates uniform random postive integers.*/ |
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.sincos: parse arg z,_,i; x=x*x; p=z; do k=2 by 2; _=-_*x/(k*(k+i)); z=z+_; if z=p then leave; p=z; end; return z |
.sincos: parse arg z,_,i; x=x*x; p=z; do k=2 by 2; _=-_*x/(k*(k+i)); z=z+_; if z=p then leave; p=z; end; return z |
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ln: procedure; parse arg x,f; call e; ig=x>1.5; is=1-2*(ig\==1); ii=0; xx=x; return .ln() |
ln: procedure; parse arg x,f; call e; ig=x>1.5; is=1-2*(ig\==1); ii=0; xx=x; return .ln() |
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.ln: do while ig&xx>1.5|\ig&xx<.5;_=e; do k=-1;iz=xx*_**-is;if k>=0&(ig&iz<1|\ig&iz>.5) then leave; _=_*_;izz=iz; end |
.ln: do while ig&xx>1.5|\ig&xx<.5;_=e; do k=-1;iz=xx*_**-is;if k>=0&(ig&iz<1|\ig&iz>.5) then leave; _=_*_;izz=iz; end |
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xx=izz;ii=ii+is*2**k;end; x=x*e**-ii-1;z=0;_=-1;p=z; do k=1;_=-_*x;z=z+_/k;if z=p then leave;p=z;end; return z+ii |
xx=izz;ii=ii+is*2**k;end; x=x*e**-ii-1;z=0;_=-1;p=z; do k=1;_=-_*x;z=z+_/k;if z=p then leave;p=z;end; return z+ii |
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/*──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────*/ |
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cos: procedure; parse arg x; x=r2r(x); a=abs(x); hpi=pi*.5; numeric fuzz min(6,digits()-3); if a=pi() then return -1 |
cos: procedure; parse arg x; x=r2r(x); a=abs(x); hpi=pi*.5; numeric fuzz min(6,digits()-3); if a=pi() then return -1 |
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if a=hpi|a=hpi*3 then return 0; if a=pi()/3 then return .5; if a=pi()*2/3 then return -.5; return .sinCos(1,1,-1) |
if a=hpi|a=hpi*3 then return 0; if a=pi()/3 then return .5; if a=pi()*2/3 then return -.5; return .sinCos(1,1,-1) |
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/*──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────*/ |
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sqrt: procedure; parse arg x; if x=0 then return 0; d=digits(); m.=9; numeric digits; numeric form; h=d+6 |
sqrt: procedure; parse arg x; if x=0 then return 0; d=digits(); m.=9; numeric digits; numeric form; h=d+6 |
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parse value format(x,2,1,,0) 'E0' with g 'E' _ .; g=g*.5'e'_%2; do j=0 while h>9; m.j=h; h=h%2+1; end /*j*/ |
parse value format(x,2,1,,0) 'E0' with g 'E' _ .; g=g*.5'e'_%2; do j=0 while h>9; m.j=h; h=h%2+1; end /*j*/ |
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