Abstract
Predicting the timing of phenological events is important in agriculture, especially high revenue products. A project sponsored by USDA-ARS had the objective of adapting a previously developed model for estimating proportions of insects in different development stages as a function of temperature (degree) and time (days) for predicting bloom in almond orchards. Data for the model normally form a two-way table of counts, with rows corresponding to sample proportions of different development stages, and columns to sampling times. The data from the almond growers, however, proved problematic in that the percentages of trees in development stages were recorded but not the counts. Maximum likelihood estimation of model parameters was possible, but the variances of the estimates depend on sample size. This thesis reports a technique developed to estimate sample sizes of multinomial and product multinomial models with known proportions when empirical proportions are available but not the counts (sample size).