The evolution of a truncated gaussian probability density through time—modelling animal liveweights after selection

• Published in: Mathematical and computer modelling 2003-12, Vol.38 (11), p.1461-1468
• Main Authors: Wake, G.C., Soboleva, T.K., Pleasants, A.B.
• Format: Article
• Language: English
• Subjects: Exact sciences and technology; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Probability and statistics; Probability theory and stochastic processes; Sciences and techniques of general use; Stochastic processes; Time-dependent probability density; Truncated distribution
• ISSN: 0895-7177; 1872-9479
• DOI: 10.1016/S0895-7177(03)90150-6

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 the heavier animals are sold for slaughter and the lighter animals retained. The demands of modern quality assurance schemes require that, given information on animal growth, the farmer is able to estimate the number of animals that would meet the specifications at some time in the future after truncation. Assuming that animal growth can be described by a linear stochastic differential equation, we derive an explicit expression for the probability density of animal Liveweights at any time 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.