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Central Limit Theorem

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

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bgonçalves
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.

    SergeM's avatar - slow icon.png
    Economy class
    Belgium
    Member #123700
    February 27, 2012
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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

        SergeM's avatar - slow icon.png
        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
          SergeM's avatar - slow icon.png
          Economy class
          Belgium
          Member #123700
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          Posted: December 31, 2014, 6:11 pm - IP Logged

          Compare to N:

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

          First column approx.

            SergeM's avatar - slow icon.png
            Economy class
            Belgium
            Member #123700
            February 27, 2012
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            Posted: December 31, 2014, 6:18 pm - IP Logged

            Last hundred:

            III1
            IIII1
            IIIII1
            IIIIII2
            IIIIIII3
            IIIIIIII5
            IIIIIIIII7
            IIIIIIIIII6
            IIIIIIIIIII9
            IIIIIIIIIIII7
            IIIIIIIIIIIII5
            IIIIIIIIIIIIII2
            IIIIIIIIIIIIIIII1


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

              Last hundred:

              III1
              IIII1
              IIIII1
              IIIIII2
              IIIIIII3
              IIIIIIII5
              IIIIIIIII7
              IIIIIIIIII6
              IIIIIIIIIII9
              IIIIIIIIIIII7
              IIIIIIIIIIIII5
              IIIIIIIIIIIIII2
              IIIIIIIIIIIIIIII1

              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.

                SergeM's avatar - slow icon.png
                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...

                    SergeM's avatar - slow icon.png
                    Economy class
                    Belgium
                    Member #123700
                    February 27, 2012
                    4035 Posts
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                    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.

                      lakerben's avatar - spherewall
                      New Mexico
                      United States
                      Member #86099
                      January 29, 2010
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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)

                      Thumbs Up

                      How about them cowboys!

                       

                       

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