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# Central Limit Theorem

Topic closed. 25 replies. Last post 2 years ago by lakerben.

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bgonÃ§alves
Brasil
Member #92564
June 9, 2010
2122 Posts
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 Posted: December 29, 2014, 7:01 pm - IP Logged

(<,>) Symbol of the greatest and smallest space
F = distance from the last draw up where the number came out
For the last time
Objective = see the average frequency of each number and then put a horizontal line
To see where the line industry groups over the numbers of the draw.

Economy class
Belgium
Member #123700
February 27, 2012
4035 Posts
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 Posted: December 31, 2014, 9:33 am - IP Logged
`How do you calculate your central limits according to the type of game?  Do you think that can be applied for example to play the Euromillions?  1  / 50 = 0,02  1 / (50 - 5) = 0,022222`
`Do you consider the order of removal of the ball?`

0,022222 is good for what?

United Kingdom
Member #162012
December 19, 2014
23 Posts
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 Posted: December 31, 2014, 1:48 pm - IP Logged

0,022222 is good for what?

Calculates the relative frequencies of the historic first , without being " deformed " this relative frequency, for example Euromillions 5/50 ( main numbers ) :

Draw N1 N2 N3 N4 N5
1       29 41 36 32 16

FrN1 (32) = 1 appearance / 1 occurrence = 1
FrN2 (16) = 1 appearance / 1 occurrence = 1
.....

Draw 400 (for example):

FrN1 (32) = 90 appearances / 3300 occurences = 0,02727

In more advanced drawings , the frequency tends to Central Limit 0,021 ... However the relative frequencies of the first drawings are 1, 0.5 , 0.09 and distorts the subsequent calculation .

A good way to estimate the relative frequencies first , is to reuse the formula of the Central Limit basis for calculating the first relative frequencies. I will recalculate the previous example but using as a basis the Central Limit formula :

FrN1 (32) = 1 appearance / 1 Occurrence + ( 50Numbers - 5Positions ) = 0.0217

.....

Draw 400 (before example):

FrN1 (32) = 90 appearances / 3300 occurences + ( 50Numbers - 5Positions ) = 0,02764

Economy class
Belgium
Member #123700
February 27, 2012
4035 Posts
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 Posted: December 31, 2014, 6:03 pm - IP Logged

Calculates the relative frequencies of the historic first , without being " deformed " this relative frequency, for example Euromillions 5/50 ( main numbers ) :

Draw N1 N2 N3 N4 N5
1       29 41 36 32 16

FrN1 (32) = 1 appearance / 1 occurrence = 1
FrN2 (16) = 1 appearance / 1 occurrence = 1
.....

Draw 400 (for example):

FrN1 (32) = 90 appearances / 3300 occurences = 0,02727

In more advanced drawings , the frequency tends to Central Limit 0,021 ... However the relative frequencies of the first drawings are 1, 0.5 , 0.09 and distorts the subsequent calculation .

A good way to estimate the relative frequencies first , is to reuse the formula of the Central Limit basis for calculating the first relative frequencies. I will recalculate the previous example but using as a basis the Central Limit formula :

FrN1 (32) = 1 appearance / 1 Occurrence + ( 50Numbers - 5Positions ) = 0.0217

.....

Draw 400 (before example):

FrN1 (32) = 90 appearances / 3300 occurences + ( 50Numbers - 5Positions ) = 0,02764

E(X)=0.1

F. last 100: between 3 and 16

I don't know where you fetched that odd calculation.

In visual:

 IIIIIIIIIIIIIIII IIIIIIIIIIIIII IIIIIIIIIIIIII IIIIIIIIIIIII IIIIIIIIIIIII IIIIIIIIIIIII IIIIIIIIIIIII IIIIIIIIIIIII IIIIIIIIIIII IIIIIIIIIIII IIIIIIIIIIII IIIIIIIIIIII IIIIIIIIIIII IIIIIIIIIIII IIIIIIIIIIII IIIIIIIIIII IIIIIIIIIII IIIIIIIIIII IIIIIIIIIII IIIIIIIIIII IIIIIIIIIII IIIIIIIIIII IIIIIIIIIII IIIIIIIIIII IIIIIIIIII IIIIIIIIII IIIIIIIIII IIIIIIIIII IIIIIIIIII IIIIIIIIII IIIIIIIII IIIIIIIII IIIIIIIII IIIIIIIII IIIIIIIII IIIIIIIII IIIIIIIII IIIIIIII IIIIIIII IIIIIIII IIIIIIII IIIIIIII IIIIIII IIIIIII IIIIIII IIIIII IIIIII IIIII IIII III
Economy class
Belgium
Member #123700
February 27, 2012
4035 Posts
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 Posted: December 31, 2014, 6:11 pm - IP Logged

Compare to N:

 2,5 X 2 XX 1,5 XXXXX 1 XXXXXXX 0,5 XXXXXXXXX X XXXXXXX 0,5 XXXXX 1 XXX 1,5 XXX 2 X 2,5 X

First column approx.

Economy class
Belgium
Member #123700
February 27, 2012
4035 Posts
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 Posted: December 31, 2014, 6:18 pm - IP Logged

Last hundred:

 III 1 IIII 1 IIIII 1 IIIIII 2 IIIIIII 3 IIIIIIII 5 IIIIIIIII 7 IIIIIIIIII 6 IIIIIIIIIII 9 IIIIIIIIIIII 7 IIIIIIIIIIIII 5 IIIIIIIIIIIIII 2 IIIIIIIIIIIIIIII 1

United Kingdom
Member #162012
December 19, 2014
23 Posts
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 Posted: January 12, 2015, 11:10 am - IP Logged

Last hundred:

 III 1 IIII 1 IIIII 1 IIIIII 2 IIIIIII 3 IIIIIIII 5 IIIIIIIII 7 IIIIIIIIII 6 IIIIIIIIIII 9 IIIIIIIIIIII 7 IIIIIIIIIIIII 5 IIIIIIIIIIIIII 2 IIIIIIIIIIIIIIII 1

I don't understand anything your system.

You asked: "I don't know where you fetched that odd calculation."

And I say: This calculation its based on Kolmogorov Relative Frequency, implemented in Euromillions and reuse for calculate the Central Limit of the Relative Frequency. With this data, you can determine that ball is very "fast" or "hot", "average" and "cold"... With Central Limit, you can determine the probability of entropy (- or +) of a ball respect of Central Limit.

There are other Central Limit (the before is the Theorical), you can obtain the Effective (or Practical) Central Limit, if you obtain the Average of Relative Frequency of all balls in the historic.

Economy class
Belgium
Member #123700
February 27, 2012
4035 Posts
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 Posted: January 12, 2015, 3:28 pm - IP Logged

I don't understand anything your system.

You asked: "I don't know where you fetched that odd calculation."

And I say: This calculation its based on Kolmogorov Relative Frequency, implemented in Euromillions and reuse for calculate the Central Limit of the Relative Frequency. With this data, you can determine that ball is very "fast" or "hot", "average" and "cold"... With Central Limit, you can determine the probability of entropy (- or +) of a ball respect of Central Limit.

There are other Central Limit (the before is the Theorical), you can obtain the Effective (or Practical) Central Limit, if you obtain the Average of Relative Frequency of all balls in the historic.

Did you not recognize the Normal Distribution?

In order to use your Central Limit you first have to count.
Any value above average is higher than average.
None, one or more values can be above the Central Limit.

Concerning the game, you did not specify whether you pick or reject the numbers that have a high frequency.
The more experiments you have, the smaller the deviation becomes. (...)

I am still looking for the point that you are trying to make, behalf of showing the formula for the Central Limit.

United Kingdom
Member #162012
December 19, 2014
23 Posts
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 Posted: January 12, 2015, 5:01 pm - IP Logged

Did you not recognize the Normal Distribution?

In order to use your Central Limit you first have to count.
Any value above average is higher than average.
None, one or more values can be above the Central Limit.

Concerning the game, you did not specify whether you pick or reject the numbers that have a high frequency.
The more experiments you have, the smaller the deviation becomes. (...)

I am still looking for the point that you are trying to make, behalf of showing the formula for the Central Limit.

Did you not recognize the Normal Distribution? -> Yes, I recognize

In order to use your Central Limit you first have to count. -> Yes, the "Absolut Frequency"

None, one or more values can be above the Central Limit. -> Can you explain this?

Concerning the game, you did not specify whether you pick or reject the numbers that have a high frequency. -> always true !, if you remove the numbers with high or low frequency , the system becomes an asymptote , so it is necessary to calculate the probability of entropy generation for balls with low or high frequency ....

The more experiments you have, the smaller the deviation becomes -> When you say "samaller" I interpreted "asymptote", but for very small tarball that the deviation always have this deviation (only it has different magnitude)

I am still looking for the point that you are trying to make, behalf of showing the formula for the Central Limit. -> I show the formula in this post http://www.lotterypost.com/member/164223

For example in one draw:

High Frequency: 5 numbers (can generate entropy)

Med-High Frequency: 20 numbers (no entropy, can generate asymptote)

Med-Low Frequency: 20 numbers (no entropy, can generate asymptote)

Low Frequency: 5 numbers (can generate entropy)

The most probably is that the balls can be pumped from Med-High/Low Frequency (because has much numbers), but High/Low Frequency is probably too, but lower, and not all number with high frequency is ideal for generate entropy...

Economy class
Belgium
Member #123700
February 27, 2012
4035 Posts
Offline
 Posted: January 12, 2015, 6:11 pm - IP Logged

Did you not recognize the Normal Distribution? -> Yes, I recognize

In order to use your Central Limit you first have to count. -> Yes, the "Absolut Frequency"

None, one or more values can be above the Central Limit. -> Can you explain this?

Concerning the game, you did not specify whether you pick or reject the numbers that have a high frequency. -> always true !, if you remove the numbers with high or low frequency , the system becomes an asymptote , so it is necessary to calculate the probability of entropy generation for balls with low or high frequency ....

The more experiments you have, the smaller the deviation becomes -> When you say "samaller" I interpreted "asymptote", but for very small tarball that the deviation always have this deviation (only it has different magnitude)

I am still looking for the point that you are trying to make, behalf of showing the formula for the Central Limit. -> I show the formula in this post http://www.lotterypost.com/member/164223

For example in one draw:

High Frequency: 5 numbers (can generate entropy)

Med-High Frequency: 20 numbers (no entropy, can generate asymptote)

Med-Low Frequency: 20 numbers (no entropy, can generate asymptote)

Low Frequency: 5 numbers (can generate entropy)

The most probably is that the balls can be pumped from Med-High/Low Frequency (because has much numbers), but High/Low Frequency is probably too, but lower, and not all number with high frequency is ideal for generate entropy...

None, one or more values can be above the Central Limit. -> Can you explain this?

There doesn't have to be any number sticking out with high frequency. It is in the randomness.

Concerning the game, you did not specify whether you pick or reject the numbers that have a high frequency. -> always true !, if you remove the numbers with high or low frequency , the system becomes an asymptote , so it is necessary to calculate the probability of entropy generation for balls with low or high frequency ....

You still don't specify. I don't have a phd in mathematics.

The winning combination can be of any composition by frequency values. You still didn't specify the choice and rejection or even the composition.

New Mexico
United States
Member #86099
January 29, 2010
11119 Posts
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 Posted: February 3, 2015, 1:12 pm - IP Logged

LEGEND:
01 => Tens Number
02 => Last contest
03 => Number of outputs / Media R / D
04 => (A) > space between contests
05 => (B) <space between contests
06=> (F) Supplement (A- (B + C)) / 3
07 => Repetitions of frequencies
08 => Greater space between contests
09 => Final (A-F)
10 => repeated Frequencies
11 => (C) Sum of frequencies
12 => (D) Qty frequencies
13 => average frequency. (C / D)