September 2017 Update

Task/Statistics-Basic/Haskell/statistics-basic.hs

@@ -1,48 +1,69 @@
-{-# LANGUAGE BangPatterns #-}
-
-import Data.Foldable
-import System.Random
+import Data.Foldable (foldl') --'
+import System.Random (randomRs, newStdGen)
+import Control.Monad (zipWithM_)
 import System.Environment (getArgs)
 
-intervals :: [(Double,Double)]
-intervals = map conv [0..9]
-    where xs = [0.0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0]
-          conv s = let { [h,l] = take 2 $ drop s xs } in (h,l)
+intervals :: [(Double, Double)]
+intervals = map conv [0 .. 9]
+  where
+    xs = [0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0]
+    conv s =
+      let [h, l] = take 2 $ drop s xs
+      in (h, l)
 
 count :: [Double] -> [Int]
-count rands = map (\iv -> foldl' (loop iv) 0 rands) intervals
-   where loop :: (Double,Double) -> Int -> Double -> Int
-         loop (lo,hi) n x | lo <= x && x < hi = n+1
-                          | otherwise         = n
-         -- ^ fuses length and filter within (lo,hi)
+count rands = map (\iv -> foldl'' (loop iv) 0 rands) intervals
+  where
+    loop :: (Double, Double) -> Int -> Double -> Int
+    loop (lo, hi) n x
+      | lo <= x && x < hi = n + 1
+      | otherwise = n
 
-data Pair a b = Pair !a !b
+-- ^ fuses length and filter within (lo,hi)
+data Pair a b =
+  Pair !a
+       !b
 
 -- accumulate sum and length in one fold
 sumLen :: [Double] -> Pair Double Double
-sumLen = fion2 . foldl' (\(Pair s l) x -> Pair (s+x) (l+1)) (Pair 0.0 0)
-  where fion2 :: Pair Double Int -> Pair Double Double
-        fion2 (Pair s l) = Pair s (fromIntegral l)
+sumLen = fion2 . foldl'' (\(Pair s l) x -> Pair (s + x) (l + 1)) (Pair 0.0 0)
+  where
+    fion2 :: Pair Double Int -> Pair Double Double
+    fion2 (Pair s l) = Pair s (fromIntegral l)
 
 -- safe division on pairs
 divl :: Pair Double Double -> Double
 divl (Pair _ 0.0) = 0.0
-divl (Pair s   l) = s / l
+divl (Pair s l) = s / l
 
 -- sumLen and divl are separate for stddev below
 mean :: [Double] -> Double
 mean = divl . sumLen
 
 stddev :: [Double] -> Double
-stddev xs = sqrt $ foldl' (\s x -> s+(x-m)^2) 0 xs / l
-   where p@(Pair s l) = sumLen xs
-         m = divl p
+stddev xs = sqrt $ foldl'' (\s x -> s + (x - m) ^ 2) 0 xs / l
+  where
+    p@(Pair s l) = sumLen xs
+    m = divl p
 
-main = do nr    <- read.head <$> getArgs
-          rands <- take nr . randomRs (0.0,1.0) <$> newStdGen
-          putStrLn $ "The mean is " ++ show (mean rands) ++ " !"
-          putStrLn $ "The standard deviation is " ++ show (stddev rands) ++ " !"
-          zipWithM_ (\iv fq -> putStrLn $ ivstr iv ++ ": " ++ fqstr fq) intervals (count rands)
-    where
-        fqstr i = replicate (if i > 50 then div i (div i 50) else i) '*'
-        ivstr (lo,hi) = show lo ++ " - " ++ show hi
+main = do
+  nr <- read . head <$> getArgs
+  -- or in code, e.g.  let nr = 1000
+  rands <- take nr . randomRs (0.0, 1.0) <$> newStdGen
+  putStrLn $ "The mean is " ++ show (mean rands) ++ " !"
+  putStrLn $ "The standard deviation is " ++ show (stddev rands) ++ " !"
+  zipWithM_
+    (\iv fq -> putStrLn $ ivstr iv ++ ": " ++ fqstr fq)
+    intervals
+    (count rands)
+  where
+    fqstr i =
+      replicate
+        (if i > 50
+           then div i (div i 50)
+           else i)
+        '*'
+    ivstr (lo, hi) = show lo ++ " - " ++ show hi
+
+-- To avoid Wiki formatting issue
+foldl'' = foldl'

Task/Statistics-Basic/Kotlin/statistics-basic.kotlin

@@ -0,0 +1,49 @@
+// version 1.1.2
+
+val rand = java.util.Random()
+
+fun basicStats(sampleSize: Int) {
+    if (sampleSize < 1) return
+    val r = DoubleArray(sampleSize)
+    val h = IntArray(10) // all zero by default
+    /*
+       Generate 'sampleSize' random numbers in the interval [0, 1)
+       and calculate in which box they will fall when drawing the histogram
+    */
+    for (i in 0 until sampleSize) {
+        r[i] = rand.nextDouble()
+        h[(r[i] * 10).toInt()]++
+    }
+
+    // adjust one of the h[] values if necessary to ensure they sum to sampleSize
+    val adj = sampleSize - h.sum()
+    if (adj != 0) {
+        for (i in 0..9) {
+            h[i] += adj
+            if (h[i] >= 0) break
+            h[i] -= adj
+        }
+    }
+
+    val mean = r.average()
+    val sd = Math.sqrt(r.map { (it - mean) * (it - mean) }.average())
+
+    // Draw a histogram of the data with interval 0.1
+    var numStars: Int
+    // If sample size > 500 then normalize histogram to 500
+    val scale = if (sampleSize <= 500) 1.0 else 500.0 / sampleSize
+    println("Sample size $sampleSize\n")
+    println("  Mean ${"%1.6f".format(mean)}  SD ${"%1.6f".format(sd)}\n")
+    for (i in 0..9) {
+        print("  %1.2f : ".format(i / 10.0))
+        print("%5d ".format(h[i]))
+        numStars = (h[i] * scale + 0.5).toInt()
+        println("*".repeat(numStars))
+    }
+    println()
+}
+
+fun main(args: Array<String>) {
+    val sampleSizes = intArrayOf(100, 1_000, 10_000, 100_000)
+    for (sampleSize in sampleSizes) basicStats(sampleSize)
+}

Task/Statistics-Basic/Perl-6/statistics-basic.pl6

@@ -5,6 +5,6 @@ for 100, 1_000, 10_000 -> $N {
     printf "stddev: %f\n", sqrt
     $mean**2 R- $N R/ [+] @data »**» 2;
     printf "%.1f %s\n", .key, '=' x (500 * .value.elems / $N)
-        for sort *.key, @data.classify: (10 * *).Int / 10;
+        for sort @data.classify: (10 * *).Int / 10;
     &say;
 }

Task/Statistics-Basic/Phix/statistics-basic.phix

@@ -0,0 +1,34 @@
+function generate_statistics(integer n)
+sequence hist = repeat(0,10)
+atom sum_r = 0,
+     sum_squares = 0.0
+
+    for i=1 to n do
+        atom r = rnd()
+        sum_r += r
+        sum_squares += r*r
+        hist[floor(10*r)+1] += 1
+    end for
+    atom mean = sum_r / n
+    atom stddev = sqrt((sum_squares / n) - mean*mean)
+
+     return {n, mean, stddev, hist}
+end function
+
+procedure display_statistics(sequence x)
+atom n, mean, stddev
+sequence hist
+    {n, mean, stddev, hist} = x
+    printf(1,"-- Stats for sample size %d\n",{n})
+    printf(1,"mean: %g\n",{mean})
+    printf(1,"sdev: %g\n",{stddev})
+    for i=1 to length(hist) do
+        integer cnt = hist[i]
+        string bars = repeat('=',floor(cnt*300/n))
+        printf(1,"%.1f: %s %d\n",{i/10,bars,cnt})
+    end for
+end procedure
+
+for n=2 to 5 do
+    display_statistics(generate_statistics(power(10,n+(n=5))))
+end for

Task/Statistics-Basic/REXX/statistics-basic.rexx

@@ -11,12 +11,11 @@ if datatype(seed,'W')    then call random ,,seed /*allow a  seed  for the  RANDO
                 #._=#._+1                        /*    ···  and bump its count.         */
                 end   /*j*/
 
-        do k=0  for 10                           /*show a histogram of the bins.        */
+        do k=0  for 10;  kp=k+1                  /*show a histogram of the bins.        */
         lr='0.'k      ;  if k==0  then lr="0  "  /*adjust for the  low range.           */
-        hr='0.'||(k+1);  if k==9  then hr="1  "  /*   "    "   "  high range.           */
-        range=lr"──►"hr' '                       /*construct the range.                 */
+        hr='0.'kp     ;  if k==9  then hr="1  "  /*   "    "   "  high range.           */
         barPC=right(strip(left(format(100*#.k/size, , 2), 5)) ,5)    /*compute the  %.  */
-        say range barPC copies('─', format(barPC*1, , 0))            /*display histogram*/
+        say lr"──►"hr' '  barPC copies('─', format(barPC*1, , 0))    /*display histogram*/
         end   /*k*/
 say
 say 'sample size = ' size;          say

Task/Statistics-Basic/Stata/statistics-basic.stata

@@ -0,0 +1,10 @@
+. clear all
+. set obs 100000
+number of observations (_N) was 0, now 100,000
+. gen x=runiform()
+. summarize x
+
+    Variable |        Obs        Mean    Std. Dev.       Min        Max
+-------------+---------------------------------------------------------
+           x |    100,000    .4991874    .2885253   1.18e-06   .9999939
+. hist x

Task/Statistics-Basic/Zkl/statistics-basic-1.zkl

@@ -0,0 +1,4 @@
+fcn mean(ns)  { ns.sum(0.0)/ns.len() }
+fcn stdDev(ns){
+   m:=mean(ns); (ns.reduce('wrap(p,n){ x:=(n-m); p+x*x },0.0)/ns.len()).sqrt()
+}

Task/Statistics-Basic/Zkl/statistics-basic-2.zkl

@@ -0,0 +1,9 @@
+reg ns;
+foreach n in (T(100,1000,10000)){
+   ns=(0).pump(n,List,(0.0).random.fp(1.0));
+   println("N:%,6d  mean:%.5f std dev:%.5f".fmt(n,mean(ns),stdDev(ns)));
+}
+foreach r in ([0.0 .. 0.9, 0.1]){  // using the last data set (10000 randoms)
+   n:=ns.filter('wrap(x){ r<=x<(r+0.1) }).len();
+   println("%.2f..%.2f:%4d%s".fmt(r,r+0.1,n,"*"*(n/20)));
+}

Task/Statistics-Basic/Zkl/statistics-basic-3.zkl

@@ -0,0 +1,13 @@
+var pipe=Thread.Pipe(); // used to connect the two threads
+fcn{ while(1){ pipe.write((0.0).random(1.0)) } }.launch();  // generator
+fcn{    // consumer/calculator
+   N:=0; M:=SD:=sum:=ssum:=0.0;
+   while(1){
+      x:=pipe.read(); N+=1; sum+=x; ssum+=x*x;
+      M=sum/N; SD=(ssum/N - M*M).sqrt();
+      if(0==N%100000)
+	 println("N:%,10d  mean:%.5f std dev:%.5f".fmt(N,M,SD));
+   }
+}.launch();
+
+Atomic.sleep(60*60);  // wait because exiting the VM kills the threads