Predicting language outcomes in children who at age two are "late talkers" is a concern of Speech Language Pathologists. Currently, there is no conclusive data allowing specialists to predict which children will outgrow their delays and which children will not. The purpose of the present study is to analyze the effect of a receptive language delay on the outcome of the slow expressive language delayed child, and determine whether or not it is a viable predictor of poor outcomes. The subject information used in this project was compiled from the data collected and reported by Paul (1991) during the Portland Language Development Project (PLDP). Children in the PLDP first participated in the longitudinal study between the ages of twenty to thirtyfour months. They were categorized as being slow in expressive language development if they produced fewer that fifty intelligible words during this age range. They were then subgrouped into an expressive-receptive delayed group if they scored more than one standard deviation below the mean on the Reynell Developmental Language Scales. Of the twenty-five subjects with complete data over the five years of the study, nineteen were considered to be solely expressively delayed, while the remaining six were classified as having both an expressive and a receptive language delay. Lee's Developmental Sentence Scoring (DSS) (1974) was used to track the subject's expressive language abilities to the age of seven. DSS scores were analyzed yearly, using the Mann-Whitney nonparametric statistical test. This would determine whether the subjects considered to be both expressively and receptively delayed were exhibiting more difficulties in their expressive language abilities than those subjects with expressive delays alone. The results of the study indicated that significant differences did not exist between the two groups. Therefore, there was insufficient evidence to conclude that a receptive language delay at twenty to thirty-four months of age is a feasible predictor of lasting expressive language delays. This leads to the recommendation that additional research be conducted focusing on areas other than receptive language abilities as being predictors of poor expressive language outcomes.

This thesis considers new methods that exploit recent developments in computer technology to address three extant problems in the area of Finance and Econometrics. The problem of Asian option pricing has endured for the last two decades in spite of many attempts to find a robust solution across all parameter values. All recently proposed methods are shown to fail when computations are conducted using standard machine precision because as more and more accuracy is forced upon the problem, round-off error begins to propagate. Using recent methods from numerical analysis based on multi-precision arithmetic, we show using the Mathematica platform that all extant methods have efficacy when computations use sufficient arithmetic precision. This creates the proper framework to compare and contrast the methods based on criteria such as computational speed for a given accuracy. Numerical methods based on a deformation of the Bromwich contour in the Geman-Yor Laplace transform are found to perform best provided the normalized strike price is above a given threshold; otherwise methods based on Euler approximation are preferred. The same methods are applied in two other contexts: the simulation of stable distributions and the computation of unit root densities in Econometrics. The stable densities are all nested in a general function called a Fox H function. The same computational difficulties as above apply when using only double-precision arithmetic but are again solved using higher arithmetic precision. We also consider simulating the densities of infinitely divisible distributions associated with hyperbolic functions. Finally, our methods are applied to unit root densities. Focusing on the two fundamental densities, we show our methods perform favorably against the extant methods of Monte Carlo simulation, the Imhof algorithm and some analytical expressions derived principally by Abadir. Using Mathematica, the main two-dimensional Laplace transform in this context is reduced to a one-dimensional problem.