Techniques for Efficient Monte Carlo Simulation. Volume 2. Random Number Generation for Selected Probability Distributions

Abstract

DISTRIBUTION STATEMENTReproduction in whole or in part is permitted for any purpose of the U.S. Government. EXECUTIVE SUMMARYMonte Carlo simulation is one of the most powerful and commonly used techniques for analyzing complex physical problems. Applications can be found in many diverse areas from radiation transport to river basin modeling. Important Navy applications include analysis of antisubmarine warfare exercises and operations, prediction of aircraft or sensor performance, tactical analysis, and matrix gaine solutions where random processes are considered to be of particular importance. The range of applications has been broadening and the size, complexity, and computational effort required have been increasing. However, such developments are expected and desirable since increased realism is concomitant with more complex and extensive problem descriptions.In recognition of such trends, the requirements for improved simulation techniques are becoming more pressing. Unfortunately, methods for achieving greater efficiency are frequently overlooked in developing simulations. This can generally be attributed to one or more of the following reasons:• Analysts usually seek advanced computer systems to perform more complex simulation studies by exploiting increased speed and/or storage capabilities. This is often achieved at a considerably increased expense.• Many efficient simulation methods have evolved for specialized applic itions. For example, some of the most impressive Monte Carlo techniques have been developed in radiation transport, a discipline that does not overlap into areas where even a small number of simulation analysts are working.• Known techniques are not developed to the point where they can be easily understood or applied by even a small fraction of the analysts who are performing simulation studies or developing simulation models.

External Sources of Water for Mercury's Putative Ice Deposits

“…2 and discussion above), we then use a Monte Carlo code to create a population of asteroids or comets with masses and orbital parameters representative of those distributions. McGrath and Irving (1975) provide an algorithm for generating random numbers from a probability distribution in histogram form. Using this algorithm along with a random number generator, we create ∼5800 Earth-crossing asteroids with diameters between 0.5 and 10 km (i.e., the current number of Earth-crossing asteroids believed to be within this size range).…”

Methods for modelling and generating probabilistic components in digital computer simulation when the standard distributions are not adequate

“…These developments are important to the whole Pearson family since beta variates can be transformed to obtain other types difficult to generate directly. Using the beta relationship, McGrath and Irving [29] give flow charts and FORTRAN subroutines for each Pearson type.…”

“…McGrath and Irving1 [29] and Barnard and Cawdery [4] point out that the constant Pi values case can also be made faster than general rectangular approximation when k is large.…”

The effect of uncertainties in rate coefficients on densities ofEregion species

“…Random numbers used in this technique were generated by an adaptation [McGrath and Irving, 1973] of the standard multiplicative congruential method [Coveyou and MacPherson, 1967]; the adaptation is independent of the computer used to generate the numbers. With the use of the Gaussian error law distribution, values of kj < 0 occur in the sampling process; the number of such values increases as s increases.…”