The best way to make and update a Multinomial distribution?

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I want to fit a distribution to a set of data I have. My questions are:



  1. How can I know the best distribution that can be fitted. The expectation is that the final distribution be a Binomial or a Multinomial distribution. (is it good to use kernel density estimation?)


  2. What is the best way to update the created distribution when a new data arrives?


Thank you!




probability probability-distributions binomial-distribution density-function




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    up vote
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    down vote

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    I want to fit a distribution to a set of data I have. My questions are:



    1. How can I know the best distribution that can be fitted. The expectation is that the final distribution be a Binomial or a Multinomial distribution. (is it good to use kernel density estimation?)


    2. What is the best way to update the created distribution when a new data arrives?


    Thank you!




    probability probability-distributions binomial-distribution density-function




    share|cite|improve this question





















      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      I want to fit a distribution to a set of data I have. My questions are:



      1. How can I know the best distribution that can be fitted. The expectation is that the final distribution be a Binomial or a Multinomial distribution. (is it good to use kernel density estimation?)


      2. What is the best way to update the created distribution when a new data arrives?


      Thank you!




      probability probability-distributions binomial-distribution density-function




      share|cite|improve this question











      I want to fit a distribution to a set of data I have. My questions are:



      1. How can I know the best distribution that can be fitted. The expectation is that the final distribution be a Binomial or a Multinomial distribution. (is it good to use kernel density estimation?)


      2. What is the best way to update the created distribution when a new data arrives?


      Thank you!





      probability probability-distributions binomial-distribution density-function





      share|cite|improve this question










      share|cite|improve this question




      share|cite|improve this question









      asked Jul 30 at 11:11









      Han

      134




      134




















          1 Answer
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          Let me try to answer your questions.



          1. How can I know the best distribution that can be fitted. The expectation is that the final distribution be a Binomial or a Multinomial distribution. (is it good to use kernel density estimation?)

          First it is a very hard question to assess which distribution best fits data if we do not know anything about it, especially since there are so many different shapes of distributions out there. Now if we focus on the binomial and multinomial distributions, we could try fitting this to the data. So we estimate the parameters of these distributions according to the data. This could for instance be done by maximum likelihood estimation.
          A way to test whether this fit is a good one is to make a qq-plot to visualize if the quantiles match. Another thing to look at is hypothesis testing. Think of the Kolmogorov-Smirnov test as a way to test whether the fitted distribution matches the emprical data. We can choose a confidence level and accept or reject the proposed distribution based on this.



          1. What is the best way to update the created distribution when a new data arrives?

          If you are doing this you are basically using Bayesian statistics. Using this if we describe a prior distribution we can update our distribution using the new data. If you are unfamiliar with this I recommend searching on Wikipedia.






          share|cite|improve this answer





















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            1 Answer
            1






            active

            oldest

            votes









            active

            oldest

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            active

            oldest

            votes








            up vote
            0
            down vote



            accepted










            Let me try to answer your questions.



            1. How can I know the best distribution that can be fitted. The expectation is that the final distribution be a Binomial or a Multinomial distribution. (is it good to use kernel density estimation?)

            First it is a very hard question to assess which distribution best fits data if we do not know anything about it, especially since there are so many different shapes of distributions out there. Now if we focus on the binomial and multinomial distributions, we could try fitting this to the data. So we estimate the parameters of these distributions according to the data. This could for instance be done by maximum likelihood estimation.
            A way to test whether this fit is a good one is to make a qq-plot to visualize if the quantiles match. Another thing to look at is hypothesis testing. Think of the Kolmogorov-Smirnov test as a way to test whether the fitted distribution matches the emprical data. We can choose a confidence level and accept or reject the proposed distribution based on this.



            1. What is the best way to update the created distribution when a new data arrives?

            If you are doing this you are basically using Bayesian statistics. Using this if we describe a prior distribution we can update our distribution using the new data. If you are unfamiliar with this I recommend searching on Wikipedia.






            share|cite|improve this answer

























              up vote
              0
              down vote



              accepted










              Let me try to answer your questions.



              1. How can I know the best distribution that can be fitted. The expectation is that the final distribution be a Binomial or a Multinomial distribution. (is it good to use kernel density estimation?)

              First it is a very hard question to assess which distribution best fits data if we do not know anything about it, especially since there are so many different shapes of distributions out there. Now if we focus on the binomial and multinomial distributions, we could try fitting this to the data. So we estimate the parameters of these distributions according to the data. This could for instance be done by maximum likelihood estimation.
              A way to test whether this fit is a good one is to make a qq-plot to visualize if the quantiles match. Another thing to look at is hypothesis testing. Think of the Kolmogorov-Smirnov test as a way to test whether the fitted distribution matches the emprical data. We can choose a confidence level and accept or reject the proposed distribution based on this.



              1. What is the best way to update the created distribution when a new data arrives?

              If you are doing this you are basically using Bayesian statistics. Using this if we describe a prior distribution we can update our distribution using the new data. If you are unfamiliar with this I recommend searching on Wikipedia.






              share|cite|improve this answer























                up vote
                0
                down vote



                accepted







                up vote
                0
                down vote



                accepted






                Let me try to answer your questions.



                1. How can I know the best distribution that can be fitted. The expectation is that the final distribution be a Binomial or a Multinomial distribution. (is it good to use kernel density estimation?)

                First it is a very hard question to assess which distribution best fits data if we do not know anything about it, especially since there are so many different shapes of distributions out there. Now if we focus on the binomial and multinomial distributions, we could try fitting this to the data. So we estimate the parameters of these distributions according to the data. This could for instance be done by maximum likelihood estimation.
                A way to test whether this fit is a good one is to make a qq-plot to visualize if the quantiles match. Another thing to look at is hypothesis testing. Think of the Kolmogorov-Smirnov test as a way to test whether the fitted distribution matches the emprical data. We can choose a confidence level and accept or reject the proposed distribution based on this.



                1. What is the best way to update the created distribution when a new data arrives?

                If you are doing this you are basically using Bayesian statistics. Using this if we describe a prior distribution we can update our distribution using the new data. If you are unfamiliar with this I recommend searching on Wikipedia.






                share|cite|improve this answer













                Let me try to answer your questions.



                1. How can I know the best distribution that can be fitted. The expectation is that the final distribution be a Binomial or a Multinomial distribution. (is it good to use kernel density estimation?)

                First it is a very hard question to assess which distribution best fits data if we do not know anything about it, especially since there are so many different shapes of distributions out there. Now if we focus on the binomial and multinomial distributions, we could try fitting this to the data. So we estimate the parameters of these distributions according to the data. This could for instance be done by maximum likelihood estimation.
                A way to test whether this fit is a good one is to make a qq-plot to visualize if the quantiles match. Another thing to look at is hypothesis testing. Think of the Kolmogorov-Smirnov test as a way to test whether the fitted distribution matches the emprical data. We can choose a confidence level and accept or reject the proposed distribution based on this.



                1. What is the best way to update the created distribution when a new data arrives?

                If you are doing this you are basically using Bayesian statistics. Using this if we describe a prior distribution we can update our distribution using the new data. If you are unfamiliar with this I recommend searching on Wikipedia.







                share|cite|improve this answer













                share|cite|improve this answer



                share|cite|improve this answer











                answered Jul 30 at 11:39









                Jan

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