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Luis A. Afonso
Posts:
4,699
From:
LIsbon (Portugal)
Registered:
2/16/05


Re: Skewness and kurtosis pvalues
Posted:
May 28, 2013 6:50 AM


Cristiano solved yet his problem: so the present post seems somewhat irrelevant/futile to this purpose. However I intend to had something in what concerns the list exactness of the Skewness/Kurtosis Critical Values he indicates, namely http://mvpprograms.com/help/mvpstats/distributions/SkewnessCriticalValues http://mvpprograms.com/help/mvpstats/distributions/KurtosisCriticalValues For n=7 these Tables, twotails test: Skewness: 1.307 (.10), 1.575 (.05), 1.856 (.02), 2.043 (.01) Kurtosis: 2.02, 3.12 (.10), 2.18, 3.84 (.05), 2.40, 4.75 (.01).
My values of frequencies are (1 million samples, 7 million values) _______0.103____0.053____0.023____0.011_______(1) _______0.097____0.054____0.019_______________ (1) In the same routine (and run) the check for the Normal values X~N(0,1) were very similar to those of Kalkulator noted by [ ] __abs(x)<1 : 0.68269___[0.68269]__ ________<2 : 0.95449___[0.95450]__ ________<3 : 0.99729___[0.99730]__
Conclusion: Even for very short samples (where errors are more likely to occur) the results (1) are quite good.
Luis A. Afonso
REM "CRISTY" CLS DEFDBL AZ pi = 4 * ATN(1) INPUT " N= "; n aw = SQR(n * (n  1)) / (n  2) bw = ((n  1) * (n + 1)) / ((n  2) * (n  3)) cw = 3 * ((n  1) * (n  1)) / ((n  2) * (n  3)) DIM x(n) DIM sk(8001), kt(8001) INPUT " How many "; many sk(0) = 1.307: sk(1) = 1.575: sk(2) = 1.856: sk(3) = 2.043 kt1(0) = 2.02: kt2(0) = 3.12 kt1(1) = 2.18: kt2(1) = 3.84 kt1(2) = 2.4: kt2(2) = 4.75 REM REM FOR j = 1 TO many LOCATE 10, 50: PRINT USING "#######"; many  j RANDOMIZE TIMER FOR i = 1 TO n: x(i) = 0: NEXT i m1 = 0 FOR i = 1 TO n aa = SQR(2 * LOG(RND)) x(i) = aa * COS(2 * pi * RND) IF ABS(x(i)) < 1 THEN one = one + 1 / n IF ABS(x(i)) < 2 THEN two = two + 1 / n IF ABS(x(i)) < 3 THEN three = three + 1 / n m1 = m1 + x(i) / n NEXT i m(2) = 0: m(3) = 0: m(4) = 0 FOR k = 2 TO 4 FOR i = 1 TO n: d = x(i)  m1 m(k) = m(k) + d ^ k / n NEXT i NEXT k sk = aw * m(3) / (m(2) ^ 1.5) kt = bw * m(4) / (m(2) * m(2)) + cw REM PRINT USING " ##.### "; sk; kt FOR g = 0 TO 3 IF ABS(sk) > sk(g) THEN u(g) = u(g) + 1 NEXT g FOR g = 0 TO 2 IF kt < kt1(g) OR kt > kt2(g) THEN v(g) = v(g) + 1 NEXT g NEXT j PRINT : PRINT : PRINT REM color 14 FOR g = 0 TO 3 PRINT USING "##.### "; u(g) / many; NEXT g PRINT COLOR 12 FOR g = 0 TO 2 PRINT USING "##.### "; v(g) / many; NEXT g PRINT : PRINT : COLOR 7 PRINT USING " #.##### "; one / many; : PRINT "[0.68269]" PRINT USING " #.##### "; two / many; : PRINT "[0.95450]" PRINT USING " #.##### "; three / many; : PRINT "[0.99730]" END



