Programs in R for Computing Truncated Cauchy Distributions

Abstract

Truncated distributions arise naturally in many industrial settings. Because of the popularity of the normal distribution, programs have been developed for computing quantities of interest of its truncated version such as the truncated mean, truncated variance and the cumulative probability. In this note, we follow up the work for the Cauchy distribution because of its recent popularity as a rival to the normal distribution. We provide programs for computing six quantities of interest (probability density function, mean, variance, cumulative distribution function, quantile function and random numbers) for any truncated Cauchy distribution: whether it is left truncated, right truncated or doubly truncated. The programs are written in R, a freely downloadable statistical software.

Key Words:

• Cauchy
• quantile
• truncated Cauchy

Additional information

Notes on contributors

Saralees Nadarajah

Saralees Nadarajah Senior Lecturer in the School of Mathematics, University of Manchester, UK. His research interests include climate modeling, extreme value theory, distribution theory, information theory, sampling and experimental designs, and reliability. He is an author/co-author of four books and has over 300 papers published or accepted. He has held positions in Florida, California, and Nebraska.

Samuel Kotz

Samuel Kotz Emeritus Professor of Statistics at University of Maryland, College Park, MD, U.S.A., and is Distinguished Professor of Statistics in the Department of Engineering Management and Systems Engineering, George Washington University, Washington, DC, USA. He received his Ph.D. degree from Cornell University. He is the senior Editor-in-Chief of the 13-volume Encyclopedia of Statistical Sciences, an author and co-author of over 300 research papers and 25 books in the field of statistics and quality control, 3 Russian-English scientific dictionaries, in particular, a volume Compendium on Statistical Distributions. He holds honorary Doctorates from Harbin Institute of Technology, China, University of Athens, Greece, and Bowling State University, U.S.A. He is a member of the Washington Academy of Sciences, Fellow of the Royal Statistical Society, Fellow of the American Statistical Association, and Fellow of the Institute of Mathematical Statistics.