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Discrete vs Continuous Distribution

Topic closed. 13 replies. Last post 3 years ago by LottoMetro.

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Posted: February 12, 2014, 7:19 pm - IP Logged

In analysiing data, which  of the Distributions is most effective, and why?

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    Posted: February 14, 2014, 11:04 am - IP Logged

    In analysiing data, which  of the Distributions is most effective, and why?

    Think of ' compressed file'(Zip), the elements of the file remains intact, but pool size(hopper) is reduced.The concept of subset is focus oriented, hence discrete random variables becomes the tenet of all workouts. Most of  statistical parameters is geared towards  Continuous random variables,which  depicts Ranges and Estimates. The  variables and outcome of lottery event is distinct, discrete  and mutually esclusive, eg, flipping a coin is either Head or Tail, there's no in between,where as taking Census or  Stock's trend is more of range measurement> percentiles,quartiles etc.  So if  continuous stats parameters like Sums, roots .... could be converted to discrete values (Indicators, trends, prediction points), then most prediction will be enhanced.

    Your thoughts on this will be appreciated.

      SergeM's avatar - slow icon.png
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      Posted: February 14, 2014, 1:03 pm - IP Logged

      Explain me how you want to get better results in predictions. Naming tools means nothing.

      Just look at the results in the simulations, how many percent of the posters actually get a full payback?

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        Posted: February 14, 2014, 3:52 pm - IP Logged

        Explain me how you want to get better results in predictions. Naming tools means nothing.

        Just look at the results in the simulations, how many percent of the posters actually get a full payback?

        You missed the intent of this topic, Discrete vs Continuous approach to data analysis, thanks for your input anyway.

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          Happyland
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          Posted: February 14, 2014, 4:09 pm - IP Logged

          For the lottery? Not sure exactly what you are asking.

          Lotteries are analyzed using discrete distributions: i.e. Poisson, binomial, and hypergeometric. We primarily use discrete in lottery because lottery consists of finite, countable variables. Percentiles, quartiles, and range has nothing to do with the distribution type....they can be measured in either one.

          There are cases when a continuous distribution is close to discrete; for instance a uniform continuous distribution will resemble a uniform discrete distribution if the variables are wide (i.e. 000 to 999). But that is because by definition a uniform distribution is one where each event has an equal probability. Personally, I don't really see how converting discrete to continuous would provide any advantage. I guess the simplest way to differ between the two is that discrete can be 5 or 6 but continuous can be 5.9668444844 to infinity. For lotteries it just makes more sense to use discrete, because a value like 5.9668444844 or a negative won't show up. If you used a continuous distribution you would have to truncate it, otherwise it will go on to infinity.

          If the chances of winning the jackpot are so slim, why play when the jackpot is so small? Your chances never change, but the potential payoff does.
          If a crystal ball showed you the future of the rest of your life, and in that future you will never win a jackpot, would you still play?

          2016: -48.28% (13 tickets) ||
          P&L % = Total Win($)/Total Wager($) - 1

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            Posted: February 14, 2014, 5:12 pm - IP Logged

            For the lottery? Not sure exactly what you are asking.

            Lotteries are analyzed using discrete distributions: i.e. Poisson, binomial, and hypergeometric. We primarily use discrete in lottery because lottery consists of finite, countable variables. Percentiles, quartiles, and range has nothing to do with the distribution type....they can be measured in either one.

            There are cases when a continuous distribution is close to discrete; for instance a uniform continuous distribution will resemble a uniform discrete distribution if the variables are wide (i.e. 000 to 999). But that is because by definition a uniform distribution is one where each event has an equal probability. Personally, I don't really see how converting discrete to continuous would provide any advantage. I guess the simplest way to differ between the two is that discrete can be 5 or 6 but continuous can be 5.9668444844 to infinity. For lotteries it just makes more sense to use discrete, because a value like 5.9668444844 or a negative won't show up. If you used a continuous distribution you would have to truncate it, otherwise it will go on to infinity.

            Thanks very much for detailed explanation of the 2 distrubutions, am bit perplexed when you said, percentiles, quartiles, which i think are statistical measurements for parameters like , Standard deviations,mean, median, sum, etc  has nothing do with distributions, how so? what tools(parameters) do you use to inteprete a said data? I understand countable variables are counted and  continuous are measured.

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              Happyland
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              Posted: February 14, 2014, 5:31 pm - IP Logged

              Thanks very much for detailed explanation of the 2 distrubutions, am bit perplexed when you said, percentiles, quartiles, which i think are statistical measurements for parameters like , Standard deviations,mean, median, sum, etc  has nothing do with distributions, how so? what tools(parameters) do you use to inteprete a said data? I understand countable variables are counted and  continuous are measured.

              "Standard deviations,mean, median, sum, etc  has nothing do with distributions, how so?"

              What I meant was that these things can be measured regardless of the distribution. If you have a set of data you can calculate all of these without even knowing whether the information follows a continuous or a discrete distribution. Distributions are useful mainly to find the central tendency of data.

              Example, you have a set of numbers: 5, 19, 32, 56, 11, 40, 16. The mean of this sample would be 25.57, the median would be 19, the standard deviation would be 18.01, the sum would be 179, the 10th percentile would be 8.6, the 3rd quartile (aka 75th percentile) would be 36, and the range would be 51. You can compute all that for any dataset without knowing the distribution. You can even approximate the population statistics based only on samples.

              I mostly use Microsoft Excel with a couple different add-ons, but also MATLAB and Maple. Regarding the lottery, I use the chi-squared test to determine if numbers are statistically significant, and I pay attention to parameters like variance (= standard deviation2) to decide which games are best.

              It may sound like mumble-jumble but stats work.  YouTube has a lot of useful videos about this stuff if you're interested.

              If the chances of winning the jackpot are so slim, why play when the jackpot is so small? Your chances never change, but the potential payoff does.
              If a crystal ball showed you the future of the rest of your life, and in that future you will never win a jackpot, would you still play?

              2016: -48.28% (13 tickets) ||
              P&L % = Total Win($)/Total Wager($) - 1

                SergeM's avatar - slow icon.png
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                Posted: February 15, 2014, 3:42 pm - IP Logged

                You mean statistical mathematics.


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                  Posted: February 15, 2014, 7:58 pm - IP Logged

                  Think of ' compressed file'(Zip), the elements of the file remains intact, but pool size(hopper) is reduced.The concept of subset is focus oriented, hence discrete random variables becomes the tenet of all workouts. Most of  statistical parameters is geared towards  Continuous random variables,which  depicts Ranges and Estimates. The  variables and outcome of lottery event is distinct, discrete  and mutually esclusive, eg, flipping a coin is either Head or Tail, there's no in between,where as taking Census or  Stock's trend is more of range measurement> percentiles,quartiles etc.  So if  continuous stats parameters like Sums, roots .... could be converted to discrete values (Indicators, trends, prediction points), then most prediction will be enhanced.

                  Your thoughts on this will be appreciated.

                  This idea seems to be plausible for data storage, coin tossing, and stocks,

                  Will this work for Poker? Jester

                   

                  On a more serious note, Data is just Data.

                  There is no need for conversion.  Conversion is an extra step.  The point is to reduce steps.

                  I prefer Data Consolidation over Data Conversion.

                  You dont need to convert anything to locate a potential indicator.

                    SergeM's avatar - slow icon.png
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                    Posted: February 18, 2014, 10:13 am - IP Logged

                    Lottobone: "Will this work for Poker? Jester"

                    Maybe with 2 aces in your hand and 2 aces on the table!

                      SergeM's avatar - slow icon.png
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                      Posted: February 18, 2014, 10:21 am - IP Logged

                      "Standard deviations,mean, median, sum, etc  has nothing do with distributions, how so?"

                      What I meant was that these things can be measured regardless of the distribution. If you have a set of data you can calculate all of these without even knowing whether the information follows a continuous or a discrete distribution. Distributions are useful mainly to find the central tendency of data.

                      Example, you have a set of numbers: 5, 19, 32, 56, 11, 40, 16. The mean of this sample would be 25.57, the median would be 19, the standard deviation would be 18.01, the sum would be 179, the 10th percentile would be 8.6, the 3rd quartile (aka 75th percentile) would be 36, and the range would be 51. You can compute all that for any dataset without knowing the distribution. You can even approximate the population statistics based only on samples.

                      I mostly use Microsoft Excel with a couple different add-ons, but also MATLAB and Maple. Regarding the lottery, I use the chi-squared test to determine if numbers are statistically significant, and I pay attention to parameters like variance (= standard deviation2) to decide which games are best.

                      It may sound like mumble-jumble but stats work.  YouTube has a lot of useful videos about this stuff if you're interested.

                      You wrote above that you use chi square test, but in fact you use a relative squared deviation frequency towards a mathematically averaged frequency for every number.

                      You made no point on why and how to take decisions. So there is no documentation on whether you increase or decrease your odds. There is no indication on how or what to pick and there is no mathematical proof to it.

                        SergeM's avatar - slow icon.png
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                        Posted: February 18, 2014, 10:25 am - IP Logged

                        In analysiing data, which  of the Distributions is most effective, and why?

                        The distributions are mathematically the same. The amount of samples determins how the distribution looks like when you make a graph. So, the answer is, there is no most effective distribution as all distributions are in fact the same. The drawing has the last word. For lottery balls you work with integer counts, not with floats. You forgot the length of eternity in your calculation. (...) Does the past influence the future? You are on an eternal time line. The lottery may exist only for a small time period.

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                          Posted: February 20, 2014, 5:14 pm - IP Logged

                          The distributions are mathematically the same. The amount of samples determins how the distribution looks like when you make a graph. So, the answer is, there is no most effective distribution as all distributions are in fact the same. The drawing has the last word. For lottery balls you work with integer counts, not with floats. You forgot the length of eternity in your calculation. (...) Does the past influence the future? You are on an eternal time line. The lottery may exist only for a small time period.

                          Hello first post BTW. Couldn't find the 'new member section'

                           

                          While I agree with you that you would work with Integers (ie for the balls) and not using decimals or floats, what about normalization of the data.

                          So for example the your numbers range from 1-47 the number/ball 33 could be represented as 0.702

                          I would think, analyising the lottery for discrete vs continuos, we would encounter the problem that numbers are just numbers an there is not context of what '2' is or '33' is.  Where as, percents or normalized data, would range from 0-1.  Where the number represented as .03 is half the number of what .06 is no matter how large your data set is.  You could have numbers/balls that range from 5-5000

                          normalized value = (ballValue/(maxVal-minVal))

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                            Happyland
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                            Posted: February 20, 2014, 5:45 pm - IP Logged

                            You wrote above that you use chi square test, but in fact you use a relative squared deviation frequency towards a mathematically averaged frequency for every number.

                            You made no point on why and how to take decisions. So there is no documentation on whether you increase or decrease your odds. There is no indication on how or what to pick and there is no mathematical proof to it.

                            Nope.

                            If the chances of winning the jackpot are so slim, why play when the jackpot is so small? Your chances never change, but the potential payoff does.
                            If a crystal ball showed you the future of the rest of your life, and in that future you will never win a jackpot, would you still play?

                            2016: -48.28% (13 tickets) ||
                            P&L % = Total Win($)/Total Wager($) - 1