An approach to trend analysis in data with special reference to cometary magnitudes

Abstract

A recent approach to trend analysis in data is introduced and developed in the context of a Pareto power-law model. The way in which theory based on the normal distribution can be modified by suitable choice of parameter and sample size to deal with general parametric families of distributions is explained with numerical examples. The Pareto distribution used by Donnison (1990, MNRAS, 245) to model the brightness (magnitude) distribution of long-period, (P > 200 yr) and short-period (P < 15 yr) comets is reanalysed in terms of this new trend approach. Overwhelming evidence is found that the brightness indices increase with discovery date for the long-period comets