Data update
This commit is contained in:
Ingy döt Net
parent
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commit
cbaf4c4b64
12390 changed files with 318560 additions and 27248 deletions
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100 REM Statistics/Normal distribution
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110 DECLARE EXTERNAL SUB NormalStats
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120 CALL NormalStats(100)
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130 PRINT
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140 CALL NormalStats(1000)
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150 PRINT
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160 CALL NormalStats(10000)
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170 PRINT
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180 END
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190 REM ***
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200 EXTERNAL SUB NormalStats (SampleSize)
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210 IF SampleSize < 1 THEN EXIT SUB
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220 DIM R(1 TO 10000)
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230 LET MaxSampleSize = UBOUND(R)
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240 IF SampleSize > MaxSampleSize THEN
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250 PRINT "Sample size too large"
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260 STOP
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270 END IF
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280 RANDOMIZE
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290 DIM H(-1 TO 10) ! all zero by default
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300 LET Sum = 0
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310 LET HSum = 0
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320 REM Gener!ate 'SampleSize' normally distributed random numbers with Mean 0.5 and standard deviation 0.25
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330 REM calculate their Sum
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340 REM and in which box they will fall when drawing the histogram
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350 FOR I = 1 TO SampleSize
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360 LET RandomNormal = COS(2 * PI * RND) * SQR(-2 * LOG(RND))
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370 LET R(I) = .5 + RandomNormal / 4
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380 LET Sum = Sum + R(I)
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390 IF R(I) < 0 THEN
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400 LET H(-1) = H(-1) + 1
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410 ELSEIF R(I) >= 1 THEN
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420 LET H(10) = H(10) + 1
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430 ELSE
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440 LET H(INT(R(I) * 10)) = H(INT(R(I) * 10)) + 1
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450 END IF
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460 NEXT I
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470 FOR I = -1 TO 10
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480 LET HSum = HSum + H(I)
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490 NEXT I
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500 REM adjust one of the H() values if necessary to ensure HSum = SampleSize
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510 LET Adj = SampleSize - HSum
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520 IF Adj <> 0 THEN
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530 FOR I = -1 TO 10
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540 LET H(I) = H(I) + Adj
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550 IF H(I) >= 0 THEN EXIT FOR
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560 LET H(I) = H(I) - Adj
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570 NEXT I
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580 END IF
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590 LET Mean = Sum / SampleSize
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600 LET Sum = 0
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610 REM Now calculate their standard deviation
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620 FOR I = 1 TO SampleSize
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630 LET Sum = Sum + (R(I) - Mean) ^ 2
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640 NEXT I
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650 LET Sd = SQR(Sum / SampleSize)
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660 REM Draw a histogram of the data with interval 0.1
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670 REM If sample size > 300 then normalize histogram to 300
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680 LET Scale = 1
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690 IF SampleSize > 300 THEN LET Scale = 300 / SampleSize
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700 PRINT "Sample size "; SampleSize
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710 PRINT USING " Mean #.###### SD #.######": Mean, Sd
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720 FOR I = -1 TO 10
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730 IF I = -1 THEN
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740 PRINT "< 0.00 : ";
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750 ELSEIF I = 10 THEN
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760 PRINT ">=1.00 : ";
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770 ELSE
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780 PRINT USING " #.## : ": I / 10;
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790 END IF
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800 PRINT USING "##### ": H(I);
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810 PRINT REPEAT$("*", ROUND(H(I) * Scale, 0))
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820 NEXT I
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830 END SUB
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func logn n .
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return log n 0
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.
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func randnorm .
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return cos (360 * randomf) * sqrt (-2 * logn randomf)
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.
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global smpl[] .
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func mean .
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for v in smpl[] : sum += v
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return sum / len smpl[]
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.
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func stddev .
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avg = mean
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for v in smpl[] : squares += (avg - v) * (avg - v)
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return sqrt (squares / len smpl[])
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.
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proc mksmpl n .
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smpl[] = [ ]
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for i to n
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v = 100 + randnorm * 15
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smpl[] &= v
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.
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.
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proc histo .
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len count[] 199
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for v in smpl[]
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ind = floor (v + 0.5)
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ind = higher 1 ind
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ind = lower 199 ind
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count[ind] += 1
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.
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n = len smpl[]
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for i = 40 to 160
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v = count[i]
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h = floor (v * 1500 / n)
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s$ = ""
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for j to h : s$ &= "*"
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print i & " " & v & " " & s$
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.
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.
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numfmt 5 4
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proc stats size .
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mksmpl size
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print "Size: " & size
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print "Mean: " & mean
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print "Stddev: " & stddev
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print ""
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histo
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print ""
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.
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stats 1000000
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(* Statistics/Normal distribution *)
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block
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(* Generates normally distributed random numbers with mean 0 and standard deviation 1 *)
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unit random_normal: function: real;
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const
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pi = 3.14159265358979;
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begin
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result := cos(2.0 * pi * random) * sqrt(-2.0 * ln(random))
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end random_normal;
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unit normal_stats: procedure (sample_size: integer);
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var
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r: arrayof real,
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sum, mean, diff, scale, sd: real,
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h: arrayof integer,
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h_sum, adj, i, j: integer;
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begin
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if sample_size < 1 then return fi;
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array r dim (1 : sample_size);
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array h dim (-1 : 10); (* all zero by default *)
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sum := 0.0;
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h_sum := 0;
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(* Generate 'sample_size' normally distributed random numbers with mean 0.5
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and standard deviation 0.25.
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Calculate their sum and in which box they will fall when drawing
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the histogram. *)
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for i := 1 to sample_size
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do
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r(i) := .5 + random_normal / 4.0;
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sum := sum + r(i);
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if r(i) < 0.0
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then h(-1) := h(-1) + 1
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else
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if r(i) >= 1.0
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then h(10) := h(10) + 1
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else h(entier(r(i) * 10)) := h(entier(r(i) * 10)) + 1
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fi
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fi
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od;
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for i := -1 to 10 do h_sum := h_sum + h(i) od;
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(* Adjust one of the h() values if necessary to ensure h_sum = sample_size *)
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adj := sample_size - h_sum;
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if adj =/= 0
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then
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for i := -1 to 10
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do
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h(i) := h(i) + adj;
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if h(i) >= 0 then exit fi;
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h(i) := h(i) - adj
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od
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fi;
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mean := sum / sample_size;
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(* Now calculate their standard deviation *)
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sum := 0.0;
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for i := 1 to sample_size
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do
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diff := r(i) - mean;
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sum := sum + diff * diff
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od;
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sd := sqrt(sum / sample_size);
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(* Draw a histogram of the data with interval 0.1
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If sample size > 300 then normalize histogram to 300 *)
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scale := 1.0;
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if sample_size > 300 then scale := 300.0 / sample_size fi;
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writeln("Sample size ", sample_size);
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writeln(" Mean ", mean: 8: 6, " SD ", sd: 8: 6);
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for i := -1 to 10
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do
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if i = -1 then write("< 0.00 : ")
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else
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if i = 10
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then write(">=1.00 : ")
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else write(" ", i / 10.0 : 4: 2, " : ")
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fi
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fi;
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write(h(i): 5, " ");
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for j := 1 to entier(h(i) * scale + .5) do write("*") od;
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writeln
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od;
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end normal_stats;
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begin
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call normal_stats(100);
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writeln;
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call normal_stats(1000);
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writeln;
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call normal_stats(10000);
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writeln;
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end;
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<?php
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// Statistics/Normal distribution
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normal_stats(100);
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echo PHP_EOL;
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normal_stats(1000);
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echo PHP_EOL;
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normal_stats(10000);
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echo PHP_EOL;
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// Generates normally distributed random numbers with $mean 0 and standard deviation 1
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function random_normal() {
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return cos(2.0 * M_PI * mt_rand() / mt_getrandmax()) *
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sqrt(-2.0 * log(mt_rand() / mt_getrandmax()));
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}
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function normal_stats ($sample_size) {
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if ($sample_size < 1) return;
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srand((double)microtime() * 1000000);
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$r = array_fill(0, $sample_size, 0);
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$h = array_fill(0, 12, 0);
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$sum = 0.0;
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$h_sum = 0;
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// Generate '$sample_size' normally distributed random numbers with $mean 0.5
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// and standard deviation 0.25
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// calculate their $sum
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// and in which box they will fall when drawing the histogram
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for ($i = 0; $i < $sample_size; $i++) {
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$r[$i] = .5 + random_normal() / 4.0;
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$sum += $r[$i];
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if ($r[$i] < 0.0)
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$h[0]++;
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else if ($r[$i] >= 1.0)
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$h[11]++;
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else
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$h[ceil($r[$i] * 10)]++;
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}
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foreach ($h as $h_item)
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$h_sum += $h_item;
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// adjust one of the $h values if necessary to ensure $h_sum = $sample_size
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$adj = $sample_size - $h_sum;
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if ($adj != 0) {
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for ($i = 0; $i <= 11; $i++) {
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$h[$i] += $adj;
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if ($h[$i] >= 0) break;
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$h[$i] -= $adj;
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}
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}
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$mean = $sum / $sample_size;
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$sum = 0.0;
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// Now calculate their standard deviation
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foreach ($r as $r_item)
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$sum += pow($r_item - $mean, 2);
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$sd = sqrt($sum / $sample_size);
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// Draw a histogram of the data with interval 0.1
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// If sample size > 300 then normalize histogram to 300
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$scale = 1.0;
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if ($sample_size > 300)
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$scale = 300.0 / $sample_size;
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echo 'Sample size '.$sample_size.PHP_EOL;
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echo ' Mean '.
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str_pad(number_format($mean, 6, '.', ''), 8, ' ', STR_PAD_LEFT).
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' SD '.
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str_pad(number_format($sd, 6, '.', ''), 8, ' ', STR_PAD_LEFT).PHP_EOL;
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$i = -1;
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foreach ($h as $h_item) {
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if ($i == -1)
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echo '< 0.00 : ';
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else if ($i == 10)
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echo '>=1.00 : ';
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else
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echo ' '.
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str_pad(number_format($i / 10.0, 2, '.', ''), 4, ' ', STR_PAD_LEFT).
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' : ';
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echo str_pad($h_item, 5, ' ', STR_PAD_LEFT).' '.
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str_repeat('*', round($h_item * $scale)).PHP_EOL;
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$i++;
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}
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}
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?>
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require "table2"
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require "io2"
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local fmt = require "fmt"
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-- Box-Muller method from Wikipedia.
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local function normal(mu, sigma)
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local u1 = math.random()
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local u2 = math.random()
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local mag = sigma * math.sqrt(-2 * math.log(u1))
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local z0 = mag * math.cos(2 * math.pi * u2) + mu
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local z1 = mag * math.sin(2 * math.pi * u2) + mu
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return {z0, z1}
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end
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local N = 100_000
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local NUM_BINS = 12
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local bins = table.rep(NUM_BINS, 0)
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local binSize = 0.1
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local samples = table.rep(N, 0)
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local mu = 0.5
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local sigma = 0.25
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for i = 0, N / 2 - 1 do
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local rns = normal(mu, sigma)
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for j = 0, 1 do
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local rn = rns[j + 1]
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local bn
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if rn < 0 then
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bn = 0
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elseif rn >= 1 then
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bn = 11
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else
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bn = rn // binSize + 1
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end
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bins[bn + 1] += 1
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samples[i * 2 + j + 1] = rn
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end
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end
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local labels = table.rep(NUM_BINS, "")
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for i = 1, NUM_BINS do
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if i == 1 then
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labels[i] = "-inf ..< 0.00 "
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elseif i < NUM_BINS then
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labels[i] = string.format("%4.2f ..< %4.2f ", binSize * (i-1), binSize * i)
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else
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labels[i] = "1.00 ... +inf "
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end
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end
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fmt.print("Normal distribution with mean %0.2f and S/D %0.2f for %,s samples:\n", mu, sigma, N)
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local title = " Range Number of samples within that range"
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io.barchart(title, 85, labels, bins, true, true)
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local m = samples:mean()
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fmt.print("\nActual mean for these samples : %0.5f", m)
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local c = #samples
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local v = (samples:sqsum() - m * m * c) / (c - 1)
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fmt.print("Actual S/D for these samples : %0.5f", math.sqrt(v))
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@ -0,0 +1,86 @@
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# Statistics/Normal distribution
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# Generates normally distributed random numbers with $mean 0 and standard deviation 1
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function Get-RandomNormal {
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return [Math]::Cos(2.0 * [Math]::PI * (Get-Random -Maximum 1.0)) * [Math]::Sqrt(-2.0 * [Math]::Log((Get-Random -Maximum 1.0)))
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}
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function Write-NormalStats {
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param ([uint32]$SampleSize)
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if ($SampleSize -lt 1) {
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return
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}
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$r = [double[]]::new($SampleSize)
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$h = [uint32[]]::new(12) # all zero by default
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$sum = 0.0
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$hSum = 0
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# Generate '$SampleSize' normally distributed random numbers with $mean 0.5 and standard deviation 0.25
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# calculate their $sum
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# and in which box they will fall when drawing the histogram
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$iTo = $SampleSize - 1
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foreach ($i in 0..$iTo) {
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$r[$i] = .5 + $(Get-RandomNormal) / 4.0
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$sum += $r[$i]
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if ($r[$i] -lt 0.0) {
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$h[0]++
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} elseif ($r[$i] -ge 1.0) {
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$h[11]++
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} else {
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$h[[Math]::Ceiling($r[$i] * 10)]++
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}
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}
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foreach ($hItem in $h) {
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$hSum += $hItem
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}
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# adjust one of the $h[] values if necessary to ensure $hSum = $SampleSize
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$adj = $SampleSize - $hSum
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if ($adj -ne 0) {
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$iTo = $h.Length - 1
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foreach ($i in 0..$iTo) {
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$h[$i] += $adj
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if ($h[$i] -ge 0) {
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break
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}
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$h[$i] -= $adj
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}
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}
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$mean = $sum / $SampleSize
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$sum = 0.0
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# Now calculate their standard deviation
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foreach ($rItem in $r) {
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$sum += [Math]::Pow($rItem - $mean, 2)
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}
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$sd = [Math]::Sqrt($sum / $SampleSize)
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# Draw a histogram of the data with interval 0.1
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# If sample size > 300 then normalize histogram to 300
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$scale = 1.0
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if ($SampleSize -gt 300) {
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$scale = 300.0 / $SampleSize
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}
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Write-Output "Sample size $SampleSize"
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Write-Output (' Mean {0,8:N6} SD {1,8:N6}' -f $mean, $sd)
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$i = -1
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foreach ($hItem in $h) {
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if ($i -eq -1) {
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$out = '< 0.00 : '
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} elseif ($i -eq 10) {
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$out = '>=1.00 : '
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} else {
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$out = ' {0,4:N2} : ' -f ($i / 10.0)
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}
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$out += ('{0,5} ' -f $hItem)
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Write-Output ($out + ('*' * [Math]::Round($hItem * $scale)))
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$i++
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}
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}
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Write-NormalStats 100
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Write-Output ""
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Write-NormalStats 1000
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Write-Output ""
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Write-NormalStats 10000
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Write-Output ""
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@ -0,0 +1,92 @@
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DECLARE FUNCTION randomNormal! ()
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DECLARE SUB normalStats (sampleSize)
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CONST pi = 3.141592653589793#
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RANDOMIZE TIMER
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CLS
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CALL normalStats(100)
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PRINT
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CALL normalStats(1000)
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PRINT
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CALL normalStats(10000)
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PRINT
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CALL normalStats(100000)
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PRINT "Press any key to quit"
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END
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SUB normalStats (sampleSize)
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IF sampleSize < 1 THEN EXIT SUB
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DIM r(1 TO sampleSize) AS SINGLE
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DIM h(-1 TO 10) AS INTEGER
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DIM sum AS DOUBLE: sum = 0!
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DIM hSum AS INTEGER: hSum = 0
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DIM i AS INTEGER
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|
||||
' Generate samples: mean 0.5, std 0.25
|
||||
FOR i = 1 TO sampleSize
|
||||
r(i) = .5 + randomNormal! / 4!
|
||||
sum = sum + r(i)
|
||||
|
||||
IF r(i) < 0! THEN
|
||||
h(-1) = h(-1) + 1
|
||||
ELSEIF r(i) >= 1! THEN
|
||||
h(10) = h(10) + 1
|
||||
ELSE
|
||||
h(INT(r(i) * 10)) = h(INT(r(i) * 10)) + 1
|
||||
END IF
|
||||
NEXT i
|
||||
|
||||
FOR i = -1 TO 10
|
||||
hSum = hSum + h(i)
|
||||
NEXT i
|
||||
|
||||
' Adjust if necessary (rounding error)
|
||||
DIM adj AS INTEGER: adj = sampleSize - hSum
|
||||
IF adj <> 0 THEN
|
||||
FOR i = -1 TO 10
|
||||
h(i) = h(i) + adj
|
||||
IF h(i) >= 0 THEN EXIT FOR
|
||||
h(i) = h(i) - adj
|
||||
NEXT i
|
||||
END IF
|
||||
|
||||
DIM mean AS DOUBLE: mean = sum / sampleSize
|
||||
|
||||
' Standard deviation
|
||||
sum = 0!
|
||||
FOR i = 1 TO sampleSize
|
||||
sum = sum + (r(i) - mean) ^ 2!
|
||||
NEXT i
|
||||
DIM sd AS DOUBLE: sd = SQR(sum / sampleSize)
|
||||
|
||||
PRINT "Sample size"; sampleSize
|
||||
PRINT
|
||||
PRINT USING " Mean #.######"; mean;
|
||||
PRINT USING " SD #.######"; sd
|
||||
PRINT
|
||||
|
||||
' Histogram (scale large samples)
|
||||
DIM numStars AS INTEGER
|
||||
DIM scale AS DOUBLE: scale = 1!
|
||||
IF sampleSize > 300 THEN scale = 300 / sampleSize
|
||||
|
||||
FOR i = -1 TO 10
|
||||
IF i = -1 THEN
|
||||
PRINT "< 0.00 : ";
|
||||
ELSEIF i = 10 THEN
|
||||
PRINT ">=1.00 : ";
|
||||
ELSE
|
||||
PRINT USING " #.## : "; i / 10;
|
||||
END IF
|
||||
|
||||
PRINT USING "##### "; h(i);
|
||||
numStars = INT(h(i) * scale + .5)
|
||||
PRINT STRING$(numStars, "*")
|
||||
NEXT i
|
||||
END SUB
|
||||
|
||||
FUNCTION randomNormal!
|
||||
randomNormal! = COS(2 * pi * RND) * SQR(-2 * LOG(RND))
|
||||
END FUNCTION
|
||||
|
|
@ -0,0 +1,82 @@
|
|||
Rebol [
|
||||
title: "Rosetta code: Statistics/Normal_distribution"
|
||||
file: %Statistics-Normal_distribution.r3
|
||||
url: https://rosettacode.org/wiki/Statistics/Normal_distribution
|
||||
author: @ldci
|
||||
needs: 3.19.0
|
||||
]
|
||||
|
||||
random/seed 1
|
||||
randMax: 2147483647 ;; max integer value
|
||||
nMax: 500000 ;; number of random values, can be modified
|
||||
|
||||
;; Normal random numbers generator using Marsaglia algorithm.
|
||||
;; Generates 2 independent series of random values in the range [-1.0, 1.0].
|
||||
generate: function [
|
||||
n [integer!] ;; number of pairs to generate
|
||||
][
|
||||
m: n * 2
|
||||
values: make vector! [f64! :m] ;; vector to hold generated values
|
||||
for i 1 m 2 [
|
||||
rsq: 0.0
|
||||
;; Repeat while radius squared is outside the unit circle or zero
|
||||
while [any [(rsq >= 1.0) (rsq == 0.0)]] [
|
||||
x: (2.0 * random randMax) / randMax - 1.0
|
||||
y: (2.0 * random randMax) / randMax - 1.0
|
||||
rsq: (x * x) + (y * y)
|
||||
]
|
||||
f: sqrt ((-2.0 * log-e rsq) / rsq)
|
||||
values/(i): x * f
|
||||
values/(i + 1): y * f
|
||||
]
|
||||
values
|
||||
]
|
||||
|
||||
;; Show histogram of the values vector
|
||||
printHistogram: function [
|
||||
values [vector!]
|
||||
][
|
||||
width: 50.0 ;; width of histogram bars
|
||||
low: -3.0 ;; lower bound of histogram
|
||||
high: 3.0 ;; upper bound of histogram
|
||||
delta: 0.1 ;; bin width
|
||||
n: values/length ;; length of data
|
||||
nbins: to integer! ((high - low) / delta) ;; number of bins (60)
|
||||
bins: make vector! [i32! :nbins] ;; initialize bins vector
|
||||
repeat i n [
|
||||
j: to integer! ((values/:i - low) / delta)
|
||||
if all [(j >= 1) (j <= nbins)] [
|
||||
bins/:j: bins/:j + 1 ;; increment bin counter
|
||||
]
|
||||
]
|
||||
maxi: bins/maximum ;; max count in any bin
|
||||
repeat j nbins [
|
||||
lbin: round/to (low + j * delta - high + 0.25) 0.01 ;; low limit for bin
|
||||
hbin: round/to (low + j + 1 * delta - high + 0.25) 0.01 ;; high limit for bin
|
||||
s: ajoin ["[" lbin " " hbin "] "] ;; bin label string
|
||||
pad s -15 ;; pad string left for alignment
|
||||
k: width * bins/:j / maxi ;; number of block characters to print
|
||||
while [k > 0] [
|
||||
append s to-char 9609 ;; append block character (unicode 9609)
|
||||
k: k - 1
|
||||
]
|
||||
append s ajoin [" " round/to (bins/:j * 100 / n) 0.01 "%"] ;; append percentage
|
||||
print s
|
||||
]
|
||||
]
|
||||
|
||||
;;********************** Main ***********************
|
||||
|
||||
print "Be patient! Generating Data and Gaussian Histogram..."
|
||||
print-horizontal-line
|
||||
|
||||
time: dt [
|
||||
values: generate nMax ;; generate nMax pairs of random values
|
||||
printHistogram values ;; print histogram of generated values
|
||||
]
|
||||
|
||||
print-horizontal-line
|
||||
print [nMax * 2 "Values processed in:" round/to third time 0.01 "sec"]
|
||||
print ["Mean: " values/mean]
|
||||
print ["STD : " values/sample-deviation]
|
||||
print-horizontal-line
|
||||
|
|
@ -0,0 +1,73 @@
|
|||
normalStats(100)
|
||||
print
|
||||
normalStats(1000)
|
||||
print
|
||||
normalStats(10000)
|
||||
print
|
||||
normalStats(100000)
|
||||
end
|
||||
|
||||
sub randomNormal()
|
||||
local u1, u2
|
||||
u1 = ran()
|
||||
u2 = ran()
|
||||
return cos(2 * pi * u1) * sqrt(-2 * log(u2))
|
||||
end sub
|
||||
|
||||
sub normalStats(n)
|
||||
local r(n), h(11)
|
||||
local i, sum, hSum, mean, sd, scale, stars
|
||||
sum = 0
|
||||
hSum = 0
|
||||
|
||||
// Generate samples: mean 0.5, std 0.25
|
||||
for i = 1 to n
|
||||
r(i) = 0.5 + randomNormal() / 4
|
||||
sum = sum + r(i)
|
||||
|
||||
if r(i) < 0 then
|
||||
h(0) = h(0) + 1
|
||||
elsif r(i) >= 1 then
|
||||
h(11) = h(11) + 1
|
||||
else
|
||||
h(int(r(i)*10)+1) = h(int(r(i)*10)+1) + 1
|
||||
fi
|
||||
next i
|
||||
|
||||
for i = 0 to 11
|
||||
hSum = hSum + h(i)
|
||||
next i
|
||||
|
||||
mean = sum / n
|
||||
|
||||
// Standard deviation
|
||||
sum = 0
|
||||
for i = 1 to n
|
||||
sum = sum + (r(i) - mean)^2
|
||||
next i
|
||||
sd = sqrt(sum / n)
|
||||
|
||||
print "Sample size ", n
|
||||
print
|
||||
print " Mean ", mean using("#.######");
|
||||
print " SD ", sd using("#.######")
|
||||
print
|
||||
|
||||
// Histogram (scale for large samples)
|
||||
scale = 1
|
||||
if n > 300 scale = 300 / n
|
||||
|
||||
for i = 0 to 11
|
||||
if i = 0 then
|
||||
print "< 0.00 : ", h(0) using("#####"), " ";
|
||||
elsif i = 11 then
|
||||
print ">=1.00 : ", h(1) using("#####");
|
||||
else
|
||||
//print using(" #.## : ##### ", (i-1)/10); h(i);
|
||||
print " ", (i-1)/10 using("#.##"), " : ", h(i) using("#####"), " ";
|
||||
fi
|
||||
|
||||
stars = int(h(i) * scale + 0.5)
|
||||
print string$(stars, "*")
|
||||
next i
|
||||
end sub
|
||||
Loading…
Add table
Add a link
Reference in a new issue