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stk_distrib_bivnorm_cdf


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 STK_DISTRIB_BIVNORM_CDF  [STK internal]



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 STK_DISTRIB_BIVNORM_CDF  [STK internal]




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stk_distrib_normal_cdf


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 STK_DISTRIB_NORMAL_CDF  [STK internal]



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 STK_DISTRIB_NORMAL_CDF  [STK internal]




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stk_distrib_normal_ei


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 STK_DISTRIB_NORMAL_EI computes the normal (Gaussian) expected improvement

 CALL: EI = stk_distrib_normal_ei (Z)

    computes the expected improvement of a standard normal (Gaussian)
    random variable above the threshold Z.

 CALL: EI = stk_distrib_normal_ei (Z, MU, SIGMA)

    computes the expected improvement of a Gaussian random variable
    with mean MU and standard deviation SIGMA, above the threshold Z.

 CALL: EI = stk_distrib_normal_ei (Z, MU, SIGMA, MINIMIZE)

    computes the expected improvement of a Gaussian random variable
    with mean MU and standard deviation SIGMA, below the threshold Z
    if MINIMIZE is true, above the threshold Z otherwise.

 REFERENCES

   [1] D. R. Jones, M. Schonlau and William J. Welch. Efficient global
       optimization of expensive black-box functions.  Journal of Global
       Optimization, 13(4):455-492, 1998.

   [2] J. Mockus, V. Tiesis and A. Zilinskas. The application of Bayesian
       methods for seeking the extremum. In L.C.W. Dixon and G.P. Szego,
       editors, Towards Global Optimization, volume 2, pages 117-129, North
       Holland, New York, 1978.

 See also stk_distrib_student_ei



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 STK_DISTRIB_NORMAL_EI computes the normal (Gaussian) expected improvement



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stk_distrib_normal_pdf


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 STK_DISTRIB_NORMAL_PDF  [STK internal]



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 STK_DISTRIB_NORMAL_PDF  [STK internal]




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stk_distrib_student_cdf


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 STK_DISTRIB_STUDENT_CDF  [STK internal]



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 STK_DISTRIB_STUDENT_CDF  [STK internal]




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stk_distrib_student_ei


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 STK_DISTRIB_STUDENT_EI computes the Student expected improvement

 CALL: EI = stk_distrib_student_ei (Z, NU)

    computes the expected improvement of a Student random variable with NU
    degrees of freedom above the threshold Z.

 CALL: EI = stk_distrib_student_ei (Z, NU, MU, SIGMA)

    computes the expected improvement of a Student random variable with NU
    degrees of freedom, location parameter MU and scale parameter SIGMA,
    above the threshold Z.

 CALL: EI = stk_distrib_student_ei (Z, NU, MU, SIGMA, MINIMIZE)

    computes the expected improvement of a Student random variable with NU
    degrees of freedom, location parameter MU and scale parameter SIGMA,
    below the threshold Z if MINIMIZE is true, above the threshold Z
    otherwise.

 REFERENCES

   [1] R. Benassi, J. Bect and E. Vazquez.  Robust Gaussian process-based
       global optimization using a fully Bayesian expected improvement
       criterion.  In: Learning and Intelligent Optimization (LION 5),
       LNCS 6683, pp. 176-190, Springer, 2011

   [2] B. Williams, T. Santner and W. Notz.  Sequential Design of Computer
       Experiments to Minimize Integrated Response Functions. Statistica
       Sinica, 10(4):1133-1152, 2000.

 See also stk_distrib_normal_ei



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 STK_DISTRIB_STUDENT_EI computes the Student expected improvement



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stk_distrib_student_pdf


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 STK_DISTRIB_STUDENT_PDF  [STK internal]



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 STK_DISTRIB_STUDENT_PDF  [STK internal]






