670 – Statistical Computing in Data Science
Statistical Calculations Through Rational Arithmetic and Conversions
Timothy Hall
PQI Consulting
When making analytical calculations with floating point real numbers it is commonly the case that even the most basic operations, such as arithmetic and conversions, produce only approximate results. The cumulative effect from such incremental approximations may quickly become problematical, producing final results that significantly differ from the exact (correct) result. However, when making those same analytical calculations with rational numbers, the results are necessarily exact (correct) at every stage of the calculation. This eliminates the effect of intermediate calculation error, so that the implementing analyst may concentrate on input data error and precision management issues. In particular, to facilitate simulations and theoretical input data possibilities, irrational numbers may be symbolically represented in the calculations and in intermediate results until a controlled approximation is needed. This paper presents an analytical framework for making error free statistical calculations using rational arithmetic and conversion operations. Several example calculations are provided to demonstrate how final result error is eliminated in all cases.