Correcting the trigonometric moments and resultant lengths for grouped circular data

Дата публикации: 10-09-2026 00:00:00

We revisit the problem of correcting the trigonometric moments and the resultant lengths that are obtained from grouped circular data. In circular measurements as elsewhere, it is common in many practical applications to aggregate the data into intervals either for convenience, or because of lack of accuracy in measuring, and then assuming that all the observations in a given interval lie at the midpoint of that interval, for calculating needed statistics. It then becomes important to ask for formulae necessary to adjust for the error introduced by such approximations, and this problem has been considered earlier in Greenwood (1959) and Mardia (1972) focusing on the first two trigonometric moments, because they are the ones used mostly in practice. The proofs provided there also rely on other outside results. We take it considerably further with our principal contributions being twofold: (i) unlike earlier derivations, we provide very simple and straightforward derivations which...

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