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Topic: Skewness and kurtosis p-values
Replies: 11   Last Post: May 28, 2013 6:50 AM

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Luis A. Afonso

Posts: 4,615
From: LIsbon (Portugal)
Registered: 2/16/05
Re: Skewness and kurtosis p-values
Posted: May 28, 2013 6:50 AM
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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, two-tails 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 A-Z
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



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