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Statistics/Normal distribution: Difference between revisions

Statistics/Normal distribution (view source)

Revision as of 19:04, 13 August 2020

105 bytes added ,  3 years ago
m
→‎{{header|REXX}}: added whitespace, changed some comments, optimized the COSine function.
m (→‎{{header|R}}: first part was not done)
m (→‎{{header|REXX}}: added whitespace, changed some comments, optimized the COSine function.)
Line 2,515:
<br>so we hoi polloi programmers have to roll our own.
<lang rexx>/*REXX program generates 10,000 normally distributed numbers (Gaussian distribution).*/
numeric digits 20 /*use 20 twenty decimal digitsdigs for accuracy.*/
parse arg n seed . /*obtain optional arguments from the CL*/
if n=='' | n=="," then n= 10000 /*Not specified? Then use the default.*/
Line 2,525:
mn= #.1; mx= mn; noise= n * .0005 /*calculate the noise: 1/20th % of N.*/
ss= 0
do j=1 for n; _= #.j; s=s+_; ss=ss+_*_ /*the sum, and the sum of squares. */
s= s + _; ss= ss + _ * _ /*the sum, and the sum of squares. */
mn= min(mn, _); mx= max(mx, _) /*find the minimum and the maximum. */
end /*j*/
!.= 0
say 'number of data points = ' aafmt(n )
say ' minimum = ' aafmt(mn )
say ' maximum = ' aafmt(mx )
say ' arithmetic mean = ' aafmt(s/n)
say ' standard deviation = ' aafmt(sqrt( ss/n - (s/n) **2) )
?mn= !.1; ?mx= ?mn /*define minimum & maximum value so far*/
parse value scrSize() with sd sw . /*obtain the (true) screen size of term*/ /*◄──not all REXXes have this BIF*/
sdE= sd - 4 /*the effective (useableusable) screen depth. */
swE= sw - 1 /* " " " " width.*/
$= 1 / max(1, mx-mn) * sdE /*$ is used for scaling depth of histo*/
do i=1 for n; ?= trunc( (#.i-mn) * $) /*calculate the relative line. */
!.?= !.? + 1 /*bump the counter. /*bump the counter. */
?mn= min(?mn, !.?); ?mx= max(?mx, !.?) /*find the minimum. and maximum*/
?mx= max(?mx, !.?) /* " " maximum. */
end /*i*/
f= swE/?mx /*limit graph to 1 full screen*/
do h=0 for sdE; _= !.h /*obtain a data point. */
if _>noise then say copies('─', trunc(_*f) ) /*display a bar of histogram. */
end /*h*/ /*[↑] use a hyphen for histo.*/
exit /*stick a fork in it, we're all done. */
/*───────────────────────────────────────────────────────────────────────────────────────────────────────────────────*/
/*──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────*/
aafmt: parse arg a@; return left('', (a@>=0) + 2 * datatype(a@, 'W'))a@ /*prepend a blank if #>=0, add 2 blanks if whole.*/
e: e = 2.7182818284590452353602874713526624977572470936999595749669676277240766303535; return e
pi: pi= 3.1415926535897932384626433832795028841971693993751058209749445923078164062862; return pi
r2r: return arg(1) // (pi() * 2) /*normalize the given angle (in radians) to ±2pi.*/
rand: return random(1, 1e5) / 1e5 /*REXX generates uniform random postive integers.*/
/*───────────────────────────────────────────────────────────────────────────────────────────────────────────────────*/
.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
ln: procedure; parse arg x,f; call e; ig= x>1.5; is= 1 -2*(ig\==1); ii= 0; xx= x; do while ig & xx>1.5 | \ig & xx<.5
/*──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────*/
ln: procedure; parse arg x,f; call_= e; ig= x>1.5;do isk= 1 -2*(ig\==1); iiiz= 0; xx=*_ x**-is; doif whilek>=0 & (ig & xx>iz<1.5 | \ig & xx<iz>.5) then leave; _= _*_; izz= iz; end; xx= izz
ii= ii +is*2**k; _end; x= x*e**-ii-1; z=0; do k_=-1; izp= xx*_ **-isz; ifdo k>=0 & (ig & iz<1 | \ig & iz>.5) then leave; _= -_*x;z=z+_/k;if izzz=p iz;then leave;p=z;end; return xx= izzz+ii
/*───────────────────────────────────────────────────────────────────────────────────────────────────────────────────*/
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
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; parseif arga=hpi x;| xa=r2r(x)hpi*3 then return 0; if a=abs(x);pi/3 hpi= pi*then return .5; numeric fuzz min(6, digits()-3); if a=pi *2/3 then return -.5; z= 1; _= 1
x= x*x; ifp= az; do k=hpi2 | aby 2; _=hpi*3 -_ then* returnx 0/ (k*(k-1)); if a z=pi/3 z then+ return_; .5; if az=pi*2/3p then returnleave; -.5 p= z; end; return .sinCos(1,1,-1)z
/*───────────────────────────────────────────────────────────────────────────────────────────────────────────────────*/
/*──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────*/
sqrt: procedure; parse arg x; if x=0 then return 0; d= digits(); m.= 9; numeric digits; numeric form; h= d+6
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*/
do k=j+5 to 0 by -1; numeric digits m.k; g=(g+x/g)*.5; end /*k*/; numeric digits d; return g/1</lang>
This REXX program makes use of &nbsp; '''scrsize''' &nbsp; REXX program (or BIF) which is used to determine the screen size of the terminal (console); &nbsp; this is to aid in maximizing the width of the horizontal histogram.
 
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