By A. C. Bajpai, Irene M. Calus, J. A. Fairley (auth.), C. N. Hewitt (eds.)
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Apart from reducing possible risk arising from round-off error, fewer digits mean fewer keys to be pressed, thus saving time and reducing opportunities of making wrong entries. In fact, the %Fe data could be even further simplified by making 0·0 I the unit, so that the values become 2,0, 5, I and 7. It would then be necessary, when s has been calculated, to convert back to the original units by multiplying by 0·01. A more detailed explanation of coding is given in Ref. 4. 5 Calculating s from a frequency table As with the arithmetic mean, calculating s from data given in the form of a frequency table is just a matter of adapting the original definition.
The approach is based around the well-known 'structural' or 'com- NONSTATIONARY TIME-SERIES ANALYSIS 49 ponent' time-series model and, like previous state-space solutions,22-24 it employs the standard Kalman filter-type l2 recursive algorithms. ) Except in the final forecasting and smoothing stages of the analysis, however, the justification for using these algorithms is not the traditional one based on 'optimality' in a prediction error or maximum likelihood (ML) sense. Rather, the algorithms outlined here are utilised in a manner which allows for straightforward and effective spectral decomposition of the time series into quasi-orthogonal components.
00085 s = 0·029 determinations of %Fe made by Laboratory B. ) Similar calculations give, for Laboratory A's results, s = 0'167, the larger value reflecting the greater amount of spread. 3 A shortcut method The formula for s can be converted into an alternative form which cuts out the step of calculating deviations from the mean. By simple algebra, it can be shown that (6) The %Fe results obtained by Laboratory B are again chosen for illustration. From Table 6, LX = 70·65 and Lx2 = 998·2879. 65 2/5 998·2879 - 998·2845 0·0034 s is then found as before.