Means and Variances of Stochastic Vector Products with Applications to Random Linear Models
Brown, Gerald G.
MetadataShow full item record
Applications in operations research often employ models which contain linear functions. These linear functions may have some components (coefficients and variables) which are random. (For instance, linear functions in mathematical programming often represent models of processes which exhibit randomness in resource availability, consumption rates, and activity levels.) Even when the linearity assumptions of these models is unquestioned, the effects of the randomness in the functions is of concern. Methods to accomodate, or at least estimate for a linear function the implications of randomness in its components typically make several simplifying assumptions. Unfortunately, when components are known to be random in a general, multivariate dependent fashion, concise specification of the randomness exhibited by the linear function is, at best, extremely complicated, usually requiring severe, unrealistic restrictions on the density functions of the random components. Frequent stipula- tions include assertion of normality, or of independence-yet, observed data, accepted collat- eral theory and common sense may dictate that a symmetric distribution with infinite domain limits is inappropriate, or that a dependent structure is definitely present. (For example, random resource levels may be highly correlated due to economic conditions, and non- negative for physical reasons.) Often, an investigation is performed by discretizing the random components at point quantile levels, or by replacing the random components by their means-methods which give a deterministic "equivalent" model with constant terms, but possibly very misleading results. Outright simulation can be used, but requires considerable time investment for setup and debugging (especially for generation of dependent sequences of pseudorandom variates) and gives results with high parametric specificity and computation cost. This paper shows how to use elementary methods to estimate the mean and variance of a linear function with arbitrary multivariate randomness in its components. Expressions are given for the mean and variance and are used to make Tchebycheff-type probability state- ments which can accomodate and exploit stochastic dependence. Simple estimation examples are given which lead to illustrative applications with (dependent-) stochastic programming models.
Management Science, 24, 2, pp. 210-216.
Rightsdefined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
Showing items related by title, author, creator and subject.
Ziomek, Lawrence J.; Sibul, Leon H. (Acoustical Society of America, 1982);Signal‐to‐interference ratio (SIR) expressions for a doubly spread target are derived for both broadband and narrow‐band transmit signals. For broadband signals, the SIR is dependent upon target and reverberation two‐frequency ...
Two models of time constrained target travel between two endpoints constructed by the application of Brownian motion and a random tour Comstock, William Justin (Monterey, California. Naval Postgraduate School, 1983-03);A target must chose a path between some origin and destination. The total travel times and the target speed are specified, and the target wishes to maximize the "randomness" of its track subject to the spatial and temporal ...
Gibbons, Deborah E. (2007-09);Objectives. I used computational models to test the relationship between interorganizational network structures and diffusion of moderate- to high-priority health information throughout a system. I examined diffusion ...