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The regression methods frequently used to estimate the parameters associated with primary moult in birds are unsatisfactory. Results obtained using least squares regression, and various ad hoc adaptations, are so obviously incorrect that many authors have fitted lines ‘by eye’ (Newton 1968, Thomas & Dartnall 1971, Elliott et al. 1976, Morrison 1976, Appleton & Minton 1978). In a comparison of seven regression methods, estimates of the average starting date varied between 29 June and 31 July, completion date between 2 and 24 October, and duration of moult between 72 and 109 days for the Redshank Tringo totonus, in spite of the very large sample of 1482 observations (Summers et al. 1983). In this paper we present a new approach to the analysis of primary moult and develop a mathematical model specifically designed for moult data.

A family of multivariate models for the occurrence/nonoccurrence of precipitation at N sites is constructed by assuming a different joint probability of events at the sites for each of a number of unobservable climate states. The climate process is assumed to follow a Markov chain. Simple formulae for first-and second-order parameter functions are derived, and used to find starting values for a numerical maximization of the likelihood. The method is illustrated by applying it to data for one site in Washington and to data for a network in the Great Plains. 558 BD Stem, R. D., and R. Coe, A model fitting analysis of rainfall data (with discussion), J. R. Star. Soc., $er. A., 147, 1-34, 1984.Waymire, E., V. K. Gupta, and I. Rodriguez-Iturbe, A spectral theory of rainfall intensity at the meso-/3 scale, Water Resour.