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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_logpdf


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 STK_DISTRIB_LOGPDF [STK internal]

 Trying to make things cleaner, until we finally develop an elegant system of
 probability distribution objects...

 INTERNAL FUNCTION WARNING:

    This function is currently considered as internal.  Please be aware that
    API-breaking changes are likely to happen in future releases.



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 STK_DISTRIB_LOGPDF [STK internal]



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stk_distrib_logpdf_grad


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 STK_DISTRIB_LOGPDF_GRAD [STK internal]

 Trying to make things cleaner, until we finally develop an elegant system of
 probability distribution objects...

 INTERNAL FUNCTION WARNING:

    This function is currently considered as internal.  Please be aware that
    API-breaking changes are likely to happen in future releases.



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 STK_DISTRIB_LOGPDF_GRAD [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_crps


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 STK_DISTRIB_NORMAL_CRPS computes the CRPS for Gaussian predictive distributions

 CALL: CRPS = stk_distrib_normal_crps (Z, MU, SIGMA)

    computes the Continuous Ranked Probability Score (CRPS) of Z with respect
    to a Gaussian predictive distribution with mean MU and standard deviation
    SIGMA.

    The CRPS is defined as the integral of the Brier score for the event
    {Z <= z}, when z ranges from -inf to +inf:

       CRPS = int_{-inf}^{+inf} [Phi((z - MU)/SIGMA) - u(z - Z)]^2 dz,

    where Phi is the normal cdf and u the Heaviside step function.  The CRPS
    is equal to zero if, and only if, the predictive distribution is a Dirac
    distribution (SIGMA = 0) and the observed value is equal to the predicted
    value (Z = MU).

 REFERENCE

   [1] Tilmann Gneiting and Adrian E. Raftery, "Strictly proper scoring
       rules, prediction, and estimation", Journal of the American
       Statistical Association, 102(477):359-378, 2007.

 See also: stk_distrib_normal_cdf, stk_predict_leaveoneout



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 STK_DISTRIB_NORMAL_CRPS computes the CRPS for Gaussian predictive distributi...



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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.

 NOTE

    Starting with STK 2.4.1, it is recommended to use stk_sampcrit_ei_eval
    instead of this function.  Be careful, however, with the "direction" of
    the improvement that you want to compute:

       EI = stk_sampcrit_ei_eval (MU, SIGMA, Z)

    computes the expected improvement *below* the threshold Z, and is thus
    equivalent to

       EI = stk_distrib_normal_ei (Z, MU, SIGMA, true)

    To compute the expected improvement *above* Z, change signs as follows:

       EI = stk_sampcrit_ei_eval (-MU, SIGMA, -Z)

 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_sampcrit_ei_eval, 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]






