How does scipy calculate the binomial CDF so fast?












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I ran scipy.stats.binom.cdf(500006, 1000000, 0.5) and it took less than a milisecond. This is crazy as binomial CDF involves summing up a bunch of binomial coefficients. What approximation algorithm goes behind the implementation? Thanks!






binomial computational-statistics scipy







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    $begingroup$


    I ran scipy.stats.binom.cdf(500006, 1000000, 0.5) and it took less than a milisecond. This is crazy as binomial CDF involves summing up a bunch of binomial coefficients. What approximation algorithm goes behind the implementation? Thanks!






    binomial computational-statistics scipy







    share|cite|improve this question









    $endgroup$















      1












      1








      1





      $begingroup$


      I ran scipy.stats.binom.cdf(500006, 1000000, 0.5) and it took less than a milisecond. This is crazy as binomial CDF involves summing up a bunch of binomial coefficients. What approximation algorithm goes behind the implementation? Thanks!






      binomial computational-statistics scipy







      share|cite|improve this question









      $endgroup$




      I ran scipy.stats.binom.cdf(500006, 1000000, 0.5) and it took less than a milisecond. This is crazy as binomial CDF involves summing up a bunch of binomial coefficients. What approximation algorithm goes behind the implementation? Thanks!






      binomial computational-statistics scipy




      binomial computational-statistics scipy






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      asked 3 hours ago









      John JiangJohn Jiang

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          There's a connection between the binomial cdf and the beta cdf. As a result, most software implementations of binomial cdf use a call to a regularized incomplete beta function. That's what scipy.stats does also, as it says in the documentation of special.bdtr (which is what gets called when you ask for a binomial cdf)



          https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.bdtr.html






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            $begingroup$

            There's a connection between the binomial cdf and the beta cdf. As a result, most software implementations of binomial cdf use a call to a regularized incomplete beta function. That's what scipy.stats does also, as it says in the documentation of special.bdtr (which is what gets called when you ask for a binomial cdf)



            https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.bdtr.html






            share|cite|improve this answer











            $endgroup$


















              4












              $begingroup$

              There's a connection between the binomial cdf and the beta cdf. As a result, most software implementations of binomial cdf use a call to a regularized incomplete beta function. That's what scipy.stats does also, as it says in the documentation of special.bdtr (which is what gets called when you ask for a binomial cdf)



              https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.bdtr.html






              share|cite|improve this answer











              $endgroup$
















                4












                4








                4





                $begingroup$

                There's a connection between the binomial cdf and the beta cdf. As a result, most software implementations of binomial cdf use a call to a regularized incomplete beta function. That's what scipy.stats does also, as it says in the documentation of special.bdtr (which is what gets called when you ask for a binomial cdf)



                https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.bdtr.html






                share|cite|improve this answer











                $endgroup$



                There's a connection between the binomial cdf and the beta cdf. As a result, most software implementations of binomial cdf use a call to a regularized incomplete beta function. That's what scipy.stats does also, as it says in the documentation of special.bdtr (which is what gets called when you ask for a binomial cdf)



                https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.bdtr.html







                share|cite|improve this answer














                share|cite|improve this answer



                share|cite|improve this answer








                edited 14 mins ago

























                answered 2 hours ago









                Glen_b♦Glen_b

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