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| Luis A. Afonso... |
 Posted: Wed May 07, 2008 8:28 pm |
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How to simulate Cauchy samples
********************************************
___Cauchy Distribution Function (From Wikipedia)
______F(x) = (1/pi) * arctan x + 1 / 2
______location (median) Density = 0
***********************************
This leads to
_________x= tan [ pi* (F – 0.5]__________(A)
(pi= 3.14159…)
Putting F = RND we are able to GENERATE samples of whichever size n having the Cauchy Density...
__________f(x) = 1 / [pi * ( 1 + x^2) ]
*********************
In order to find FRACTILES of the median:
__1___Using (A) synthesize the sample 1 sized n. Find its MEDIAN, w (1)
__2___Memorizing
Raking into account that (QBASIC) the indexed variables
___2a) Preparing the index:
____ i = Int (1000 * w (1)) + 4000
_____IF i <0 THEN i=0
_____IF i>8000 RHEN i=8000
___2b) Memorizing; _____W (i) = W (i) + 1.
:__3____After performing 400´000 times (for example) the calculations above indicted find the quantiles (for example 0.025 and 0.975).
RESULTS:
Limits of the 95% C.I. of Cauchy MEDIANS (as it was shown on Apr. 24, 2008 11:30 AM)
___n=5_______+/-2.012
_____7_________ 1.535
_____9_________ 1.274
____11_________ 1.110
____13_________ 0.989
____15_________ 0.905
____17_________ 0.838
(400´000 samples)
****************
HISTORY
This job was a John Smith/ Jack Tomsky challenge (trap): THE IDIOTS SUPPOSED THAT I WAS UNABLE TO SIMULATE CAUCHY SAMPLES.
WHY?
FOLLOWING ITS DEFICIENT EDUCATION, THEY THOUGH BECAUSE THE MEAN IT IS NOT DEFINED I DID STUCK.
AS USUALY ON ALL STATISTICAL MATTERS THEY IGNORED COMPLETELY THAT THE POSITION PARAMETER IS NOT THE MEAN BUT THE MEDIAN (located on x=0).
THEREFORE THE JOB COULD BE SATISFATORYLY ACCOMPLISHED AND THEY WORTH, ONCE MORE, THE
______EMPHATIC DONKEYS.
Once more they show to have not sufficient expertise to self-nominate MODERATOR.
*************************
Luis Amaral Afonso (The Moderator Destroyer) |
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| Jack Tomsky... |
| Posted: Thu May 08, 2008 1:54 am |
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Quote: How to simulate Cauchy samples
********************************************
___Cauchy Distribution Function (From Wikipedia)
______F(x) = (1/pi) * arctan x + 1 / 2
______location (median) Density = 0
***********************************
This leads to
_________x= tan [ pi* (F – 0.5]__________(A)
(pi= 3.14159…)
Putting F = RND we are able to GENERATE samples of
whichever size n having the Cauchy Density...
__________f(x) = 1 / [pi * ( 1 + x^2) ]
*********************
In order to find FRACTILES of the median:
__1___Using (A) synthesize the sample 1 sized n. Find
its MEDIAN, w (1)
__2___Memorizing
Raking into account that (QBASIC) the indexed
variables
___2a) Preparing the index:
____ i = Int (1000 * w (1)) + 4000
_____IF i <0 THEN i=0
_____IF i>8000 RHEN i=8000
___2b) Memorizing; _____W (i) = W (i) + 1.
:__3____After performing 400´000 times (for example)
the calculations above indicted find the quantiles
(for example 0.025 and 0.975).
RESULTS:
Limits of the 95% C.I. of Cauchy MEDIANS (as it was
shown on Apr. 24, 2008 11:30 AM)
___n=5_______+/-2.012
_____7_________ 1.535
_____9_________ 1.274
____11_________ 1.110
____13_________ 0.989
____15_________ 0.905
____17_________ 0.838
(400´000 samples)
****************
HISTORY
This job was a John Smith/ Jack Tomsky challenge
(trap): THE IDIOTS SUPPOSED THAT I WAS UNABLE TO
SIMULATE CAUCHY SAMPLES.
WHY?
FOLLOWING ITS DEFICIENT EDUCATION, THEY THOUGH
BECAUSE THE MEAN IT IS NOT DEFINED I DID STUCK.
AS USUALY ON ALL STATISTICAL MATTERS THEY IGNORED
COMPLETELY THAT THE POSITION PARAMETER IS NOT THE
MEAN BUT THE MEDIAN (located on x=0).
THEREFORE THE JOB COULD BE SATISFATORYLY ACCOMPLISHED
AND THEY WORTH, ONCE MORE, THE
______EMPHATIC DONKEYS.
Once more they show to have not sufficient expertise
to self-nominate MODERATOR.
*************************
Luis Amaral Afonso (The Moderator Destroyer)
These are not confidence intervals on the median. Since you're assuming that the population median is known to be zero, the confidence interval for the median is [0, 0] for all confidence levels.
Jack (moderator) |
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| Luis A. Afonso... |
| Posted: Thu May 08, 2008 2:50 am |
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Jack Tomsky/John Smith wrote:
*** These are not confidence intervals on the median. Since you're assuming that the population median is known to be zero, the confidence interval for the median is [0, 0] for all confidence levels. Jack (moderator) ***
***************************+
My response
Those that make confusion betwen a parameter and the Distribution of its Sample Distribution do not WORTH TO BE ALIVE, much less to self-nominate Moderator.(WUAU; WHAU, WHAU)
The values are accurate 95% CONFIDENCE INTERVALS, all Statisticians are WELL AWARE.
DO READ SOMETHING ABOUT INSTEAD TO SPLIT NONSENSE!!!
Luis Amaral Afonso (The Moderator Destroyer) |
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| John Smith... |
| Posted: Thu May 08, 2008 4:18 am |
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Adumbo,
Since you cannot explain why your "confidence intervals" do not rely on sample information, you are guilty of this offense. When do you plan to stop being alive?
John
Quote: Those that make confusion betwen a parameter and the
Distribution of its Sample Distribution do not WORTH
TO BE ALIVE, |
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| licas_ at (no spam) hotmail.com... |
| Posted: Thu May 08, 2008 5:37 am |
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John Smith escreveu:
Quote: Adumbo,
Since you cannot explain why your "confidence intervals" do not rely on sample information, you are guilty of this offense. When do you plan to stop being alive?
John
Those that make confusion betwen a parameter and the
Distribution of its Sample Distribution do not WORTH
TO BE ALIVE,
The chain of facts is simple
__1__The DKW theorem states that the Empirical Distribution of a test
Statistics can so close we want to de Distibution Function, DF
__2__ The DF of the test is sufficient to get Critical Values defining
the
NO REJECTION REGION,
__3__What allows us to attain the Test Decision : not to have
sufficient evidence to reject H0, or, the alternative: to have
sufficient evidence to reject it.
Luis Amara Afonso ( The Moderator Destroyer) |
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| Luis A. Afonso... |
| Posted: Thu May 08, 2008 5:59 am |
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I said:
*** The chain of facts is simple
__1__The DKW theorem states that the Empirical Distribution of a test statistics can so close we want to de Distribution Function, DF
__2__ The DF of the test is sufficient to get Critical Values defining the NO REJECTION REGION,
__3__What allows us to attain the Test Decision: not to have sufficient evidence to reject H0, or, the alternative: to have sufficient evidence to reject it. ***
Your job (happily I not mine) is
__a) Showing that the DKW inequality is WRONG,
OR
__b) To accept the above result but proving that the DF is not sufficient to get Critical Values
OR
__c) Accept 1 and 2 and justify that Test Decision COULD NOT BE OBTAINED from the Distribution Function (of the Test Statistics).
_________À VOTRE CHOIX, MONSIEUR.
Luis Amaral Afonso ( The Moderator Destroyer) |
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| John Smith... |
| Posted: Thu May 08, 2008 7:44 am |
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Dear Adumbo,
Show me how the sample median plays a role in your confidence intervals for the median.
John 9 Smith |
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| Luis A. Afonso... |
| Posted: Thu May 08, 2008 8:13 am |
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All is explinrd in my:
May 8, 2008 2:28 AM post (The 1st in the thread)
Luis Amatal Afonso [ The Moderator Destroyer] |
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| Luis A. Afonso... |
| Posted: Thu May 08, 2008 9:58 am |
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I remind that 10-12 years ago, I was invited by my Institute’s Director (Lisbon, Portugal) to lecture a brief course in data processing. The attendants were people finishing High School (12th school year). In spite of Test Statistics wasn’t exactly included in the syllabus; I had the chance to teach something about. In order to transmit the no deterministic nature of all Statistics Science I asked they think if it was possible to find out how many flips one can perform in order to state a coin is fair, H0 : p( heads up) = 0.5).
Also the sitting dead case was a very appreciated picture of that the absence of evidence is not an evidence of absence.
It was really a pity that Jack Tomsky/ John Smith were not attending precisely this lesson.
Luis Amaral Afonso (The Moderator Destroyer) |
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| Luis A. Afonso... |
| Posted: Fri May 09, 2008 8:08 pm |
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*************************************
Cauchy MEDIAN Confidence Intervals , 2 tails
(4´000´000 samples, each line)
__n__________5%__________1%signf
__5________+/-2.014_____+/-3.752___
__7__________ 1.533_______ 2.584___
__9__________ 1.272_______ 2.022___
_11__________ 1.108_______ 1.700___
_13__________ 0.990_______ 1.482___
_15__________ 0.905_______ 1.330___
_17__________ 0.838_______ 1.214___
_19__________ 0.782_______ 1.122___
_21__________ 0.738_______ 1.049___
_23__________ 0.698_______ 0.986___
_25__________ 0.666_______ 0.936___
(Seemly, these sample sizes the Critical Values show pronounced asymptotical tendency).
****************************************
Luis Amaral Afonso |
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| John Smith... |
| Posted: Sat May 10, 2008 8:30 am |
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How wonderful! Confidence intervals that make no use of sample data. How does he do it? Adumbo is a magician. Give this man a Fields Medal or a Nobel Prize.
John % Smith |
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| Luis A. Afonso... |
| Posted: Sat May 10, 2008 9:16 am |
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Why they do not publish their thoughts?
The worse consequence is that they not get that must re-think what Statistics is. Jack Tomsky is a one more eloquent example. If one has not full conscience, complete conscience, that Probability is in the realm of RANDOMNESS, and out of it there is no Statistics, Jack Tomsky would never was caught in such BRUNDLES as, for example:
__a)____The Null Hypotheses can be proved true
__b)____H0: m=0 if rejected means that the parameter m is truly ZERO.
__c)____The of asymptotical values use are always correct whatever the sizes evolved in the Hypotheses Tests,
__d)___The dependence critical values on sample sizes (for a given alpha) should be monotonous increasing,
__e)___The sample statistics (even if parameters are evaluated from data) must follow asymptotically given Distribution (cf. Jarque - Bera Test and the Chi-squared, two degrees of freedom),
__f)____The Empirical Distribution Function of a Test Statistics (because is obtained through a sample) is not able to provide critical Values.
If the sample is representative, what it’s somewhat dutiful (Jack Tomsky, John Smith, Bob Ling, Yurra) it can be asserted that Statistical learning (including TEACHERS) in USA has low quality indeed.
I do not know why the above brilliant minds DO NOT SUBMIT A PAPER TO A SERIOUS STATISTICAL JOURNAL stating that the LILLIEFORS´S TEST IS AN ENOURMS FRAUD because. . . ? WHY?
Luis Amaral Afonso (The Moderator Destroyer) |
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| Luis A. Afonso... |
| Posted: Sat May 10, 2008 11:16 am |
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Jack Smith – John Smith’s, about MC has two origins:
___Firstly of all they are not used READ LITERATURE (even the ABSTRACTS),
___They want NOT to analyze closely the point on discussion.
At this point I uncover (at the Readers behalf);
____WHY the Lilliefors paper is correct along with that treating the Jarque-Bera test, both obtained through Monte Carlo?
BECAUSE, it’s clear, they are rigorously (or almost) NOT DEPENDENT ON SETTING PARAMETERS VALUES.
___Lilliefors´s use the REDUCCED OBSERVATIONS y= (xj – mean) /s (m=sample mean, s=sample SD)
___Jarque-Bera´s because sample Skewness is divided by the sample SD, the sample EXCESS KURTOSIS (kurtosis minus 3) divided by SD too.
These features are not fortuity: they must be doing in order that be general whatever the Normal Distribution.
(This very important feature wasn’t even found by Bob Ling, Yurra, Jack Tomsky, John Smith, by clear incapacity to THINK).
*************
Note: Monte Carlo usefulness is not restricted to a complete parameterized problem, like the indicated above: particular laws can be considered too, obviously.
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THE CAUCHY CONFIDENCE INTERVALS FOR THE MEDIANS
The sample items underlying law has no parameters at all:
__________ f(x) * pi = 1/ (1+x^2)
(pi = 3.14159…= 0.5 * perimeter / radius ratio whatever circumference)
Luis Amaral Afonso (The Moderator Destroyer) |
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| John Smith... |
| Posted: Sat May 10, 2008 5:49 pm |
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See the above confidence intervals posted by Adumbo. Notice that they do not depend on the sample data. It's a miracle!!!!!
John K Smith |
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