Level sets and minimum volume sets of probability density functions

✍ Scribed by Javier Nuñez Garcia; Zoltan Kutalik; Kwang-Hyun Cho; Olaf Wolkenhauer

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 299 KB
• Volume: 34
• Category: Article
• ISSN: 0888-613X
• DOI: 10.1016/s0888-613x(03)00052-5

✦ Synopsis

Summarizing the whole support of a random variable into minimum volume sets of its probability density function is studied in the paper. We prove that the level sets of a probability density function correspond to minimum volume sets and also determine the conditions for which the inverse proposition is verified. The distribution function of the level cuts of a density function is also introduced. It provides a different visualization of the distribution of the probability for the random variable in question. It is also very useful to prove the above proposition. The volume k of the minimum volume sets varies according to its probability a: smaller volume implies lower probability and vice versa and larger volume implies larger probability and vice versa. In this context, 1 À a is the error of an erroneously classification of a new observation inside of the minimum volume set or corresponding level set. To decide the volume and/or the error of the level set that will serve to summarize the support of the random variable, a a À k plot is defined. We also study the relation of the minimum volume set approach with random www.elsevier.com/locate/ijar