Context. Monitoring the behaviour of animals can provide early warning signs of disease or indicate loss of appetite. Also, an understanding of the variation in behaviours among animals and their distributions is essential for meaningful statistical inference. Therefore, quantifying the variation of behaviours is of both biological and statistical interest. Aim. The objectives of this study were to determine the distributions and quantify the variation among animals with respect to the times spent grazing, ruminating, idling, walking, and licking. Methods. The activities of 147 (male = 67, female = 80) Merino lambs at 10-11 months of age on a commercial farm in Edenhope, Victoria, Australia were recorded for 26 days, using ActiGraph accelerometer sensors attached to the left side of the sheep's muzzle. The male and female sheep were kept in separate paddocks. A Support Vector Machine algorithm was used to differentiate sheep behaviour into six categories: grazing, ruminating, idling, walking, licking, and other activities. The distributions of behaviours were analysed using energy statistics-based tests and Generalised Additive Models for Location, Scale, and Shape (GAMLSS). Different distributions were compared using Akaike Information Criterion (AIC) values. Key results. Among the distributions that were considered, we found that times spent ruminating in both male and female sheep populations as well as idling in male sheep were best described by the skew exponential type 2 distribution. Grazing, walking and licking behaviours were best described by the Box-Cox t distribution. The distribution of time spent grazing was symmetrical and unimodal in males, and adequately modelled by a normal distribution, but the distribution in females had a prominent left skew. Also, we found that females typically grazed for a longer time than males. However, males spent more time ruminating than grazing. Conclusions. The time spent by the animal in each activity varied during the day. Within each population, the variation among animals in the time spent grazing was best described by a Box-Cox t distribution. Implications. This study has enhanced our understanding of grazing behaviour and will facilitate more appropriate analyses of the causes of variation among animals in grazing behaviour.

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