5 research outputs found
Optimizing an objective function under a bivariate probability model
The motivation of this paper is to obtain an analytical closed form of a quadratic objective function arising from a stochastic decision process with bivariate exponential probability distribution functions that may be dependent. This method is applicable when results need to be offered in an analytical closed form without double integrals. However, the study only applies to cases where the correlation coefficient between the two variables is positive or null. A stochastic, stationary objective function, involving a single decision variable in a quadratic form is studied. We use a primitive of a bivariate exponential distribution as first expressed by Downton (1970) and revisited in Iliopoulos (2003). With this primitive, optimization of objective functions in Operations Research, supply chain management or any other setting involving two random variables, or calculations which involve evaluating conditional expectations of two joint random variables are direct. We believe the results can be extended to other cases where exponential bivariates are encountered in economic objective function evaluations. Computation algorithms are offered which substantially reduce computation time when solving numerical examples
Optimizing an objective function under a bivariate probability model
The motivation of this paper is to obtain an analytical closed form of a quadratic objective function arising from a stochastic decision process with bivariate exponential probability distribution functions that may be dependent. This method is applicable when results need to be offered in an analytical closed form without double integrals. However, the study only applies to cases where the correlation coefficient between the two variables is positive or null. A stochastic, stationary objective function, involving a single decision variable in a quadratic form is studied. We use a primitive of a bivariate exponential distribution as first expressed by Downton [Downton, F., 1970. Bivariate exponential distributions in reliability theory. Journal of Royal Statistical Society B 32, 408–417] and revisited in Iliopoulos [Iliopoulos, George., 2003. Estimation of parametric functions in Downton’s bivariate exponential distribution. Journal of statistical planning and inference 117, 169–184]. With this primitive, optimization of objective functions in Operations Research, supply chain management or any other setting involving two random variables, or calculations which involve evaluating conditional expectations of two joint random variables are direct. We believe the results can be extended to other cases where exponential bivariates are encountered in economic objective function evaluations. Computation algorithms are offered which substantially reduce computation time when solving numerical examples
Optimizing an objective function under a bivariate probability model
The motivation of this paper is to obtain an analytical closed form of a quadratic
objective function arising from a stochastic decision process with bivariate exponential
probability distribution functions that may be dependent. This method is
applicable when results need to be offered in an analytical closed form without
double integrals. However, the study only applies to cases where the correlation
coefficient between the two variables is positive or null. A stochastic, stationary
objective function, involving a single decision variable in a quadratic form is studied.
We use a primitive of a bivariate exponential distribution as first expressed
by Downton (1970) and revisited in Iliopoulos (2003). With this primitive, optimization
of objective functions in Operations Research, supply chain management
or any other setting involving two random variables, or calculations which involve
evaluating conditional expectations of two joint random variables are direct. We
believe the results can be extended to other cases where exponential bivariates are
encountered in economic objective function evaluations. Computation algorithms
are offered which substantially reduce computation time when solving numerical
examples
A comment on "Optimizing an objective function under a bivariate probability model"
This note provides simpler, shorter and more general formulas of the product moments considered by Brusset and Temme [Brusset, X., Temme, N.M., 2007. Optimizing an objective function under a bivariate probability model. European Journal of Operational Research 179, 444-458].Decision analysis Downton's bivariate exponential distribution Product moments