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Science Forum Index » Statistics - Math Forum » Towards to test asymmetry...
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| Luis A. Afonso... |
 Posted: Mon Jul 14, 2008 3:50 pm |
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Towards to test asymmetry
After my successfully * replication * of the Jarque-Bera critical values as they are presented in Literature, I felt that something could be performed about to see how the parameters could be got by NO-Parametric procedures, specifically in what concerns SKEWNESS, S.
Suppose that I *gauge* S by means of U such that
____ U = sqrt ( A*A + B*B)
where
____ A = (Q.80 - Q.50) / (Q.50 - Q.20)
____ B = (Q.90 - Q.50) / (Q.50 - Q.10)
notation
____ Q.z is such that F(X) = .z, the fractil of the Distribution under test.
___Lemma
___ if dF/dx is a symmetrical probability with median = 0, then the U = sqrt(2) =1.4142…
Some mathematical expectation values , E(U), from a symmetrical distribution X~N(0,1):n
_____n______E(U)______differences
____20_____1.811______
____30_____1.664______(0.147)
____40_____1.596______(0.068)
____50_____1.560______(0.036)
____60_____1.554______(0.026)
____70_____1.513______(0.021)
the number of simulations was not very large (40´000). In consequence the relative error 0.5% leads to retain only two decimal places: 1.81, 1.66, 1.60, 1.56, 1.55, 1.51.
Personal computers are not sufficiently fast to attain accurate values: data ordering (by brute force) is very time consumer.
However in accordance with my values the asymptotic value 1.41 seems to be perfectly attainable.
Luis Amaral Afonso |
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| John Smith... |
| Posted: Mon Jul 14, 2008 6:17 pm |
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Adumbo, you forgot to post your stupid code. Or are you afraid we'll find more of your great coding examples like
*********
the sample standard deviation can be calculated by Sumsq(Xi)/n rather than Sumsq(Xi-xbar)/(n-1).
THREAD: Another Error in Afonso's Confidence Interval Code THREAD STARTED: Apr 2 2007, 8:14 am
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BWAHAHAHAHA
John Smith |
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| licas_ at (no spam) hotmail.com... |
| Posted: Mon Jul 14, 2008 6:47 pm |
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On Jul 15, 5:17 am, John Smith <jsmith_... at (no spam) hotmail.com> wrote:
Quote: Adumbo, you forgot to post your stupid code. Or are you afraid we'll find more of your great coding examples like
*********
the sample standard deviation can be calculated by Sumsq(Xi)/n rather than Sumsq(Xi-xbar)/(n-1).
THREAD: Another Error in Afonso's Confidence Interval Code THREAD STARTED: Apr 2 2007, 8:14 am
**************
BWAHAHAHAHA
John Smith
My response
YOU ARE UNABLE TO SAY WHATEVER
CONSISTENT, Jack Tomsky, against your oponent, * only * R. A. Fisher,
that said , not using the SWING, SWING,
SHRINK, you are so fertile , DIRECTLY AND CLEARLY (firstly because it
was a MAN, not a WORM, secondly he was a scieniist not a
UNIVERSITY CLERK) that the Null Hypotheses
cannot be accepted but only failed to be
rejected.
I obtained this statement from a Reader
from which, contrarily to you a notorious LIAR, I have no reason not
to trust him.
TO THE FIGHT : Jack Tomsky went to the Hospital in order doctors find
how many
bones he have yet not broken.
Luis Amaral Afonso [The moderator destroyer] |
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| licas_ at (no spam) hotmail.com... |
| Posted: Tue Jul 15, 2008 10:38 am |
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On Jul 15, 6:16 pm, John Smith <jsmith_... at (no spam) hotmail.com> wrote:
Quote: Adumbo,
Where is your stupid BASIC program?
You are afraid to show it, aren't you?
John Smith
ESTUPID ARE YOU Jack Tomsky: YOUR PROGRAM GAVE WRONG MATH.
EXPECTATION VALUES SINCE
ARE GROWING WITH SIZE AND THEY DO NOT APPROACH
TO SQRT(2) = 1.414...
YOR ARE UNABLE T POGRAMING WHATEVER BECAUSE ARE TO STUPID TO.
LUIS AMARAL aFONSO [THE MODERATOR DESTROYER] |
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| licas_ at (no spam) hotmail.com... |
| Posted: Tue Jul 15, 2008 10:41 am |
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On Jul 15, 9:38 pm, "lic... at (no spam) hotmail.com" <lic... at (no spam) hotmail.com> wrote:
Quote: On Jul 15, 6:16 pm, John Smith <jsmith_... at (no spam) hotmail.com> wrote:
Adumbo,
Where is your stupid BASIC program?
You are afraid to show it, aren't you?
John Smith
ESTUPID ARE YOU Jack Tomsky: YOUR PROGRAM GAVE WRONG MATH.
EXPECTATION VALUES SINCE
ARE GROWING WITH SIZE AND THEY DO NOT APPROACH
TO SQRT(2) = 1.414...
YOR ARE UNABLE T POGRAMING WHATEVER BECAUSE ARE TO STUPID TO.
LUIS AMARAL aFONSO [THE MODERATOR DESTROYER]
___TOO STUPID TO DO SUH A THING.
___lUIS |
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| Luis A. Afonso... |
| Posted: Wed Jul 16, 2008 1:55 pm |
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Another (candidate) to Test Statistics
Given the samples X~ N(0, 1) : n
Retaining the Quantiles:
____A = (Q.80 - Q.50) / (Q.20 - Q.50)
____B = (Q.90 - Q.50) / (Q.10 -Q.50)
now the test statistics
____QW = | A / B|
___F(QW) = u________D.F.__________
___________n = 20__________________
__u_____0.05___0.95___ 0.025___0.975_
_QW___ 0.488__1.791__ 0.419___2.080__
___________n = 100________________
__ u_____0.05___0.95___0.025___0.975_
__QW___0.742__1.316__0.702___1.393__
These last values are somewhat interesting because
_____R = (1.316 - 0.742 ) / (1.393 - 0.702) =
______ = 0.831
is practically the ratio 1.645 / 1.960 = 0.839 of the semi-amplitude of the corresponding * central * intervals of the Normal Distribution Function. Is this fact a symptom that QW has asymptotically a normal shape? Even for not too large sample sizes note that R(n=20) = 0.784.
(Those that claim Monte Carlo worthless was much better to them to be quiet).
Luis Amaral Afonso |
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