Calculating double integral with incomplete gamma function (numerically)












1












$begingroup$


I need to calculate a double integral on two variables ($b_0$ and $b_1$) in a function that includes a gamma incomplete function such as :



$int_{Bbb R} frac{1}{eta} (lambda e^{b_{0} + b_{1}z_{1}})^{-1/eta} gammaleft(frac{1}{eta}, lambda e^{b_{0} + b_{1}z_{1}} (t^*)^eta right) frac{1}
{(2pi) left| boldsymbol{Sigma}right|^{1/2}};; e^{
-frac{1}{2}left(boldsymbol{b}-boldsymbol{mu}right)^topboldsymbol{Sigma}^{-1}left(boldsymbol{b}-boldsymbol{mu}right)
} db_0b_1$



The other variables in the function ($lambda$, $eta$...) are specified, $z$ is a vector.
I am looking for a numerical resolution.



I already did some unsuccessful attempts in R.



Any advice to help me ? Thanks !






integration numerical-methods indefinite-integrals gamma-function







share|cite|improve this question











$endgroup$

















    1












    $begingroup$


    I need to calculate a double integral on two variables ($b_0$ and $b_1$) in a function that includes a gamma incomplete function such as :



    $int_{Bbb R} frac{1}{eta} (lambda e^{b_{0} + b_{1}z_{1}})^{-1/eta} gammaleft(frac{1}{eta}, lambda e^{b_{0} + b_{1}z_{1}} (t^*)^eta right) frac{1}
    {(2pi) left| boldsymbol{Sigma}right|^{1/2}};; e^{
    -frac{1}{2}left(boldsymbol{b}-boldsymbol{mu}right)^topboldsymbol{Sigma}^{-1}left(boldsymbol{b}-boldsymbol{mu}right)
    } db_0b_1$



    The other variables in the function ($lambda$, $eta$...) are specified, $z$ is a vector.
    I am looking for a numerical resolution.



    I already did some unsuccessful attempts in R.



    Any advice to help me ? Thanks !






    integration numerical-methods indefinite-integrals gamma-function







    share|cite|improve this question











    $endgroup$















      1












      1








      1





      $begingroup$


      I need to calculate a double integral on two variables ($b_0$ and $b_1$) in a function that includes a gamma incomplete function such as :



      $int_{Bbb R} frac{1}{eta} (lambda e^{b_{0} + b_{1}z_{1}})^{-1/eta} gammaleft(frac{1}{eta}, lambda e^{b_{0} + b_{1}z_{1}} (t^*)^eta right) frac{1}
      {(2pi) left| boldsymbol{Sigma}right|^{1/2}};; e^{
      -frac{1}{2}left(boldsymbol{b}-boldsymbol{mu}right)^topboldsymbol{Sigma}^{-1}left(boldsymbol{b}-boldsymbol{mu}right)
      } db_0b_1$



      The other variables in the function ($lambda$, $eta$...) are specified, $z$ is a vector.
      I am looking for a numerical resolution.



      I already did some unsuccessful attempts in R.



      Any advice to help me ? Thanks !






      integration numerical-methods indefinite-integrals gamma-function







      share|cite|improve this question











      $endgroup$




      I need to calculate a double integral on two variables ($b_0$ and $b_1$) in a function that includes a gamma incomplete function such as :



      $int_{Bbb R} frac{1}{eta} (lambda e^{b_{0} + b_{1}z_{1}})^{-1/eta} gammaleft(frac{1}{eta}, lambda e^{b_{0} + b_{1}z_{1}} (t^*)^eta right) frac{1}
      {(2pi) left| boldsymbol{Sigma}right|^{1/2}};; e^{
      -frac{1}{2}left(boldsymbol{b}-boldsymbol{mu}right)^topboldsymbol{Sigma}^{-1}left(boldsymbol{b}-boldsymbol{mu}right)
      } db_0b_1$



      The other variables in the function ($lambda$, $eta$...) are specified, $z$ is a vector.
      I am looking for a numerical resolution.



      I already did some unsuccessful attempts in R.



      Any advice to help me ? Thanks !






      integration numerical-methods indefinite-integrals gamma-function




      integration numerical-methods indefinite-integrals gamma-function






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Jan 25 at 19:41









      clathratus

      5,1151338




      5,1151338










      asked Jan 25 at 14:37









      Flora GrappelliFlora Grappelli

      83




      83






















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