Error Distribution in Navigation

Extract

In an earlier paper the present writer drew attention to the distinction between mixed and aggregated distributions. Incidentally, two minor mis-statements in that paper should be corrected. The first sentence in the last paragraph of section 2 (page 72) should read ‘As σ₂/σ₁ (=k say) tends to either zero or infinity, X/σ increases indefinitely; whilst for k nearer unity, X/σ is smaller’. Also the last line of the Appendix should not terminate with ‘X/σ = 3·724’ but with ‘X/σ→∞’.

Mixed distributions arise when for example an error occurs either from one distribution with probability p, or from another with probability 1–p, as in a set of position line errors due sometimes to one and sometimes to the other of a pair of observers of differing precision. An aggregate distribution occurs when the error consists of, say, two sub-errors, one from each of the two distributions; as when Captain Flint marks the chart and Long John subsequently reads it.