Evolution of a truncated Gaussian density
by
Graeme C. Wake
University of Canterbury
Coauthors: T.K.Soboleva, A.B.Pleasants

The form of the probability density derived from the evolution in time of a previously truncated frequency distribution of animal liveweights is of interest in animal husbandry. Truncated frequency distributions arise when selection is practised, for example in animal breeding a group may be split and the heaviest animals retained, or when harvesting the lightest animals will be retained. Assuming that that animal growth over the short term can be described by a linear stochastic differential equation we derive using a Fokker- Planck equation for the evolving probability density function an explicit expression for it after the truncation of an initial Gaussian density. It is shown that this probability density converges rapidly to a Gaussian density, so that after about 20 days of typical growth rates for lambs the resulting density is practically indistinguishable from Gaussian.

Date received: May 12, 1998