| operator | Q | sample |
|---|---|---|
| comb[n,m] | k) comb:{(*/1f*y#|!1+x)%*/1f+!y} | comb[8;3] .. 56f (0f for y>x) |
| std (deviation) | std:{sqrt (sum l*l:x-avg x)%-1+count x} | std 1+til 6 .. 1.87 |
| variance | varp:{i*i:std x} | varp 1+til 6 .. 3.5 |
| GAUSS |
g:{abs (neg x>0f)+(1f%sqrt 2f*pi)*(exp -0.5*x*x)*t*0.31938153+t*-0.356563782+ .. .. t*1.781477937+t*-1.821255978+1.330274429*t:1f%1f+0.2316419*abs x} | g 0 .. 0.5 (pi:acos -1) |
| GAUSSinverse(9-digit precision) |
/static data a1:-39.69683028665376;a2:220.9460984245205;a3:-275.9285104469687 a4:138.3577518672690;a5:-30.66479806614716;a6:2.506628277459239 b1:-54.47609879822406;b2:161.5858368580409;b3:-155.6989798598866 b4:66.80131188771972;b5:-13.28068155288572 c1:-7.784894002430293e-03;c2:-3.223964580411365e-01;c3:-2.400758277161838 c4:-2.549732539343734;c5:4.374664141464968;c6:2.938163982698783 d1:7.784695709041462e-03;d2:3.224671290700398e-01;d3:2.445134137142996;d4:3.754408661907416 pl:0.02425;ph:1f-pl /rational approximation lower region:(x>0f)&x < pl icnd1:{q:sqrt@-2f*log x;(c6+q*c5+q*c4+q*c3+q*c2+q*c1)%1f+q*d4+q*d3+q*d2+q*d1} /Rational approximation for central region:(p<=ph) and p >= pl icnd2:{r:q*q:x-0.5;(q*a6+r*a5+r*a4+r*a3+r*a2+r*a1)%1+r*b5+r*b4+r*b3+r*b2+r*b1} /Rational approximation for upper region:(x<1f) and x > ph icnd3:{q:sqrt -2f*log 1-x;neg (c6+q*c5+q*c4+q*c3+q*c2+q*c1)%1f+q*d4+q*d3+q*d2+q*d1} pf1:{where (x>0f) and x < pl} pf2:{where not (x>ph) or x < pl} pf3:{where (x<1f) and x > ph} k)igauss:{j:x;p1:pf1 x;p2:pf2 x;p3:pf3 x;if[0<#p1;j:@[j;p1;:;icnd1 j@p1]];if[0<#p2;j:@[j;p2;:;icnd2 j@p2]];if[0<#p3;j:@[j;p3;:;icnd3 j@p3]];:j} /example s:0.889 0.991 0.00045 0.4 0.99991 0.777 0.5 0.993 igauss s .. 1.221227 2.365618 -3.320054 -0.2533471 3.745549 0.7621005 0 2.457263 | igauss enlist 0.75 .. ,0.6744898 |
| covp .. covariance | covp:{(sum(x-avg x)*y-avg y)%-1+count x} | covp . (x;y) |
| corrp .. correlation | corrp:{(sum i*j)%sqrt(sum j*j:y-avg y)*sum i*i:x-avg x} | corrp . (x;y) |
| indep .. independency of random variables (T-distributed) | indep:{c*sqrt (-2+count first x)%1-c*c:corrp . x} | indep@(x;y) .. |
| regr .. lin.regression | regr:{(avg y-i*avg x),i:((std y)%std x)*corrp . (x;y)} (or just use y!m) | regr . (x;y) .. (y ord,slope) |
| regrTest .. regression test (T distributed) | regrTest:{((sqrt (-2f+count x)%(a*a:std y)-u*u:t*i))*(i:std x)*abs z-t:last regr . (x;y)} | regrTest . (x;y;z) |
| marg .. marginal distribution (KHI squared) | marg:{sum (t*t:u-raze c)%u:(prd each i cross sum 1f*c:flip x)%sum i:sum x} | marg M |
| hypp .. testing of hypothetical probabilities(KHI squared) | hypp:{sum (i*i:y-l)%l:(count y)#x*sum y} | hypp . (P;x) |
| dtt .. double T-test (T distributed) | dtt:{((avg y)-avg x)*sqrt (1f%r*((varp x)*u-1f)+(varp y)*v-1f)*(-2f+r:u+v)*(v:count y)*(u:count x)} | dtt . (x;y) |
| bdt .. bonded test .. | bdt: {std y-x} | bdt . (x;y) |
| dsg .. double sided gauss avg test (T distributed) | dsg:{abs (x-avg y)*(sqrt count y)%std y} | dsg . (M;x) |
| regrp .. polynomial regression |
regrp:{u:x+1;r:sum each w:(enlist (count y)#1f),prds (2*x)#enlist 1f*y;b:u {1 rotate x}\r;s:u#u#'b; :raze (inv s)$flip enlist 1f*sum flip (u#enlist z)*u#w;} | regrp . (n;x;y) |