Mathematical Sciences: Inferences Concerning the Mean of Negative Binomial Populations

这项研究的目的是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。待开发的估计类型和测试程序在很大程度上类似于正态分布产生的数据的类型和测试程序。廉价计算能力的存在使这项工作成为可能。这项研究将产生适用于分析许多类型的“计数”数据的统计方法，包括例如，汽车事故、通信故障和不断变化的人口规模。分析这些数据的标准做法是使用数学近似，只有当研究的项目数达到无穷大时才有效。这项研究的影响将是提供一组准确的统计工具，以便不必依赖这些近似值。

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.