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Topic:
Skewness (Gumbel data) comparison by simulation
Replies:
1
Last Post:
Apr 2, 2014 7:16 AM



Luis A. Afonso
Posts:
4,758
From:
LIsbon (Portugal)
Registered:
2/16/05


Skewness (Gumbel data) comparison by simulation
Posted:
Apr 1, 2014 7:36 PM


Introduction Even a Distribution with zero skewness (symmetrical) the random samples shows values that are somewhat smaller or larger than this value, the imprecision going less and less when the sample size increases. We intend to compare the observed value with those the different Gumbel (A, B) Distributions do show, A and B varying at given intervals, in order that we assure we can reject that the sample could be drawn from them. More directly we will find by random simulation what sample size should be as large that only a small proportion of samples skewness, the current 5%, are less than that a list of values the skewness is characterized. The sample sizes were 150 (50) 350 , 0 <= A, B >= 1. We found: Prob. ( Observ. skewness  Gumbel(A, B) skewness) < 0.05 Results __n= 150___<= 1.75__n= 200___<= 1.69__n=250___ <= 1.65 __n=300___ <=1.61 The number of samples involved was 4000, therefore we do not reject H0: same skewness than Gumbel (A, B) since the number of values does not exceed 200 approx. A detailed example (2 attempts) __n=150 ______________bound= 1.75___________1.73____ __(0.00 , 0.00)__0.045__0.045________0.051__0.055 __(_____, 0.50)__0.049__0.049________0.050__0.049 __(_____, 1.00)__0.044__0.046________0.048__0.050 __(0.50 , 0.00)__0.049__0.047________0.050__0.053 __(_____, 0.50)__0.046__0.045________0.050__0.049 __(_____, 1.00)__0.046__0.045________0.054__0.050 __(1.00 , 0.00)__0.050__0.044________0.052__0.056 __(_____, 0.50)__0.051__0.046________0.049__0.050 __(_____, 1.00)__0.053__0.052________0.051__0.050
Luis A. Afonso
REM "ANTIGO" CLS PRINT " <ANTIGO> (5TIMESG) " DEFDBL AZ RANDOMIZE TIMER PRINT " 5 Bounds "; FOR gh = 1 TO 5 bnd(gh) = 1.77 + .02 * gh : REM adapted to the case NEXT gh INPUT " size = "; size REM DIM X(size) REM all = 4000 REM FOR inspec = 1 TO 5 COLOR inspec + 1 PRINT USING " under test 95% fractil ###.## "; bnd(inspec) REM FOR u = 0 TO 1 STEP .5: A = u FOR v = 0 TO 1 STEP .5: B = v REM outt = 0 FOR j = 1 TO all mi = 0 FOR i = 1 TO size 22 rn = RND IF rn < .000001 THEN GOTO 22 X(i) = A  B + LOG(LOG(rn)) mi = mi + X(i) / size NEXT i m2 = 0: m3 = 0 FOR vi = 1 TO size: d = X(vi)  mi m2 = m2 + d * d / size m3 = m3 + d * d * d / size NEXT vi sk = m3 / (m2 ^ 1.5) IF sk < bnd(inspec) THEN outt = outt + 1 NEXT j IF outt > .05 * all THEN GOTO 25 PRINT USING "(##.## ##.##) #.### "; A; B; outt / all; REM 25 outt = 0 NEXT v REM NEXT u PRINT NEXT inspec REM END



