Department of Mathematics Colloquium
|Estimation of moments such as the mean and
variance of populations is generally carried out through sample
estimates. Given normality of the parent population, the distribution
of sample mean and sample variance is straightforward. However, when
normality cannot be assumed, inference is usually based on
approximations through the use of the Central Limit theorem.
Furthermore, the data generated from many real populations may be
naturally bounded; i.e., weights, heights, etc. Thus, a normal
population, with its infinite bounds, may not be appropriate, and the
distribution of sample mean and variance is not obvious. Using Bayesian
analysis and maximum entropy, procedures are developed which produce
distributions for the sample mean, as well as combined mean and
variance. These methods require no assumptions on the form of the
parent distribution or the size of the sample and inherently make use
of existing bounds.