Walck C. Handbook on statistical distributions for experimentalists

University of Stockholm, 2007, - 202 p.In experimental work e.g. in physics one often encounters problems where a standard statistical probability density function is applicable. It is often of great help to be able to handle these in different ways such as calculating probability contents or generating random numbers.For these purposes, there are excellent textbooks in statistics. However, when it comes to actual applications it often turns out to be hard to find detailed explanations in the literature ready for implementation. This work has been collected over many years in parallel with actual experimental work. In this way some material may be “historical” and sometimes be na¨ıve and have somewhat clumsy solutions not always made in the mathematically most stringent may. We apologize for this but still hope that it will be of interest and help to people who are struggling to find methods to solve their statistical problems in making real applications and not only learning statistics as a course.Even if one has the skill and may be able to find solutions it seems worthwhile to have easy and fast access to formulæ ready for application. Similar books and reports exist but we hope the present work may compete in describing more distributions, being more complete, and including more explanations of relations given.The material could most probably have been divided more logically but we have chosen to present the distributions in alphabetic order. In this way, it is more of a handbook than a proper textbook. After the first release, the report has been modestly changed. This is the last modification 10 September 2007.Bernoulli Distribution.
Beta distribution.
Binomial Distribution.
Binormal Distribution.
Cauchy Distribution.
Chi-square Distribution.
Compound Poisson Distribution.
Double-Exponential Distribution.
Doubly Non-Central F-Distribution.
Doubly Non-Central t-Distribution.
Error Function.
Exponential Distribution.
Extreme Value Distribution.
F-distribution.
Gamma Distribution.
Generalized Gamma Distribution.
Geometric Distribution.
Hyperexponential Distribution.
Hypergeometric Distribution.
Logarithmic Distribution.
Logistic Distribution.
Log-normal Distribution.
Maxwell Distribution.
Moyal Distribution.
Multinomial Distribution.
Multinormal Distribution.
Negative Binomial Distribution.
Non-central Beta-distribution.
Non-central Chi-square Distribution.
Non-central F-Distribution.
Non-central t-Distribution.
Normal Distribution.
Pareto Distribution.
Poisson Distribution.
Rayleigh Distribution.
Student’s t-distribution.
Triangular Distribution.
Uniform Distribution.
Weibull Distribution.
Appendix A: The Gamma and Beta Functions.
Appendix B: Hypergeometric Functions.
Mathematical Constants.