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Publication Details
AFRICAN RESEARCH NEXUS
SHINING A SPOTLIGHT ON AFRICAN RESEARCH
computer science
Level sets and minimum volume sets of probability density functions
International Journal of Approximate Reasoning, Volume 34, No. 1, Year 2003
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Description
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 λ of the minimum volume sets varies according to its probability α: smaller volume implies lower probability and vice versa and larger volume implies larger probability and vice versa. In this context, 1 - α 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 α - λ plot is defined. We also study the relation of the minimum volume set approach with random set theory when α is a random variable and extend the most specific probability-possibility transformation proposed in [System Theory, Knowledge Engineering and Problem Solving, in: Fuzzy Logic: State of the Art, vol. 12, Kluwer, 1993, pp. 103-112] to continuous piece-wise strictly monotone probability density functions. © 2003 Elsevier Inc. All rights reserved.
Authors & Co-Authors
Núñez García, J.
United Kingdom, Manchester
The University of Manchester
Kutalik, Zoltán
Hungary, Budapest
Eötvös Loránd Tudományegyetem
Cho, Kwang-hyun
South Korea, Ulsan
University of Ulsan
Germany, Rostock
Universität Rostock
Wolkenhauer, Olaf
United Kingdom, Manchester
The University of Manchester
Statistics
Citations: 44
Authors: 4
Affiliations: 4
Identifiers
Doi:
10.1016/S0888-613X(03)00052-5
ISSN:
0888613X