Mathematical Sciences: Inferences Concerning the Mean of Negative Binomial Populations

本研究旨在为负二项分布产生的数据开发一套广泛的统计估计和假设检验程序。要开发的估计和测试程序的类型在很大程度上类似于由正态分布产生的数据的现有类型。廉价的计算能力使这项工作成为可能。这项研究将产生适合于分析许多类型的“计数”数据的统计方法，包括，例如，汽车事故，通信故障和人口规模的变化。分析这些数据的标准做法是使用数学近似值，这种近似值只有在研究的项目数量趋于无穷大时才有效。这项研究的影响将是提供一套准确的统计工具，使这些近似值不需要依赖。

This research aims at developing an extensive collection of statistical estimates and hypotheses testing procedures for data generated by the negative binomial distribution. The types of estimates and testing procedures to be developed are, for the most part, analogous to those that exist for data generated by a normal distribution. This work is made possible by the existence of inexpensive computational power. This research will produce the statistical methodology appropriate for analyzing many types of "counting" data including, for example, automobile accidents, communication failures, and a changing population's size. The standard practice for analyzing these data is to use mathematical approximations that are only valid as the number of items studied goes to infinity. The impact of this research will be to provide a collection of accurate statistical tools so that these approximations need not be relied upon.