DEVELOPMENT OF BINARY DIGITS THAT ARE SUFFICIENTLY ACCURATE FOR SIMULATIONS AND OTHER USES.
Abstract
Desired is a set of very nearly random binary digits (very closely represent independent flips of an ideal coin with sides 0 and 1). Available is m X n array of approximately random binary digits obtained experimentally. No one of these digits is necessarily independent of any of the others but the level of dependence among rows is very small. A method is given for compounding these digits to obtain a smaller set that is much more nearly random. The randomness of a set of digits is measured by its 'maximum bias.' A set is very nearly random if its maximum bias is very small. A maximum bias for compounded digits is determined from: The compounding method, the largest contribution to the maximum bias from within rows, and the largest contribution from the dependence among rows (very small). The maximum bias for a compounded set can be very small (even when the maximum bias for the initial set is quite large) but has a lower bound depending on the bias contribution from dependence among rows. One approach is oriented toward minimizing m for a given maximum bias for the compounded set, so that obtaining the initial set is simplified. Another approach is oriented toward having the number of compounded digits a reasonably large fraction of the number in the initial set. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 31, 1970
- Accession Number
- AD0706361
Entities
People
- Grace J. Kelleher
- John E. Walsh
Organizations
- Southern Methodist University