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Estimation of the quantile, mean, and variability of populations is generally done
by means of sample estimates. Given normality of the parent population, the distribution
of sample mean and sample variance is straightforward. However, when normality cannot
be assured, 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 any specified quantile, such as the median,
is not obvious.
Using Bayesian Analysis and Maximum Entropy, procedures are developed which produce
distributions for any specified quantile, the mean, and combined mean and standard
deviation.
These methods require no assumptions on the form of the parent distribution, or the
size of the sample, and inherently make use of bounds which exist.
Demonstration of these analyses will be presented, using apple-harvest data collected
from Southern Idaho.
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