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Topic: Range/stdv.dev. ratio for Normal data
Replies: 0

 Luis A. Afonso Posts: 4,758 From: LIsbon (Portugal) Registered: 2/16/05
Range/stdv.dev. ratio for Normal data
Posted: Nov 27, 2012 2:53 PM

Range/stdv.dev. ratio for Normal data

Results (trials 1, 2, 3 and literature: P. G. Hoel, Introduction to Mathematical Statistics.

_________Trial-1___2______3______ Bibl.___

__N=2____1.128__1.129__1.129____ 1.128__
____ 3____1.693__1.694__1.692 ____1.693__
____ 4____2.058__2.059__2.059____ 2.059__
____ 5____2.326__2.326__2.326____ 2.326__
___ 10____3.078__3.077__3.078____ 3.078__
___ 50____4.499__4.498__4.498____ 4.498__
__ 100____5.016__5.016__5.016____ 5.015__

My values were obtained by a.sigma.

Hoel´s data is well represented by a 4th polynomial in log´s. See below K0.

Luis A. Afonso

REM "a.sigma"
CLS
PRINT
PRINT " Amplitude/sigma RATIO "
PRINT
INPUT " size (df) "; n
pi = 4 * ATN(1)
RANDOMIZE TIMER
ali = 1000000
REM
FOR j = 1 TO ali
REM
LOCATE 10, 50: PRINT USING "#######"; ali - j
max = -400: min = 400
FOR i = 1 TO n
a = RND
aa = SQR(-2 * LOG(a))
x = 0 + aa * 1 * COS(2 * pi * RND)
IF x < min THEN min = x
IF x > max THEN max = x
NEXT i
d = max - min
mean = mean + d / ali
NEXT j
PRINT USING " #.### "; mean
END

REM "K0"
CLS
DEFDBL A-Z
a = .00799
b = 1.77861
c = -.2549
d = 3.06241 * .01
e = -1.7097 * .001
REM
FOR x = 2 TO 100
u = LOG(x)
y = a + b * u + c * u ^ 2 + d * u ^ 3 + e * u ^ 4
PRINT USING "### #.### "; x; y;
NEXT x
END