Statistical modelling and (original) (raw)

The fundamental problem addressed in this thesis is the problem of constructing confidence limits for mean or totals in finite populations, when the underlying distribution is highly skewed and contains a substantial proportion of zero values. This situation is often encountered in statistical applications such as statistical auditing, reliability, insurance, meteorology and biostatistics. The motivating example underlying this research is that of auditing (see the report published by the National Academy Press entitled "Statistical Models and Analysis in Auditing", Panel on Non-standard Mixtures of Distributions 1989), where interest is focused on computing the confidence bounds for the true total error amount. In such populations the use of the classical survey-sampling estimators such as the mean-per-unit, the difference, the ratio or regression, based on the normality assumption of the sampling distribution of the estimates, has been found unreliable, (e.g. Stringer 1963, Kaplan 1973, and Neter and Loebbecke 1975, 1977). Several alternative methods have been proposed, of which the Stringer bound (Stringer 1963), is the most widely used. This bound, while overcoming the unreliability problem of the classical estimators, has been found to be extremely conservative.