# Econstudentlog

## Statistical Models for Proportions and Probabilities

“Most elementary statistics books discuss inference for proportions and probabilities, and the primary readership for this monograph is the student of statistics, either at an advanced undergraduate or graduate level. As some of the recommended so-called ‘‘large-sample’’ rules in textbooks have been found to be inappropriate, this monograph endeavors to provide more up-to-date information on these topics. I have also included a number of related topics not generally found in textbooks. The emphasis is on model building and the estimation of parameters from the models.

It is assumed that the reader has a background in statistical theory and inference and is familiar with standard univariate and multivariate distributions, including conditional distributions.”

The above quote is from the the book‘s preface. The book is highly technical – here’s a screencap of a page roughly in the middle:

Although I’ll not talk a lot about what the book was about (not only because it might be hard for some readers to follow, I should point out, but also because detailed coverage would take a lot more time than I’d be willing to spend on this stuff), I decided to add a few links to relevant stuff he talks about in the book. Quite a few pages in the book are spent on talking about the properties of various distributions, how to estimate key parameters of interest, and how to construct confidence intervals to be used for hypothesis testing in those specific contexts.

Some of the links below deal with stuff covered in the book, a few others however just deal with stuff I had to look up in order to understand what was going on in the coverage:

Inverse sampling.
Binomial distribution.
Hypergeometric distribution.
Multinomial distribution.
Binomial proportion confidence interval. (Coverage of the Wilson score interval, Jeffreys interval, and the Clopper-Pearson interval included in the book).
Fisher’s exact test.
Marginal distribution.
Fischer information.
Moment-generating function.
Factorial moment-generating function.
Delta method.
Multidimensional central limit theorem (the book applies this, but doesn’t really talk about it).
Matrix function.
McNemar’s test.