Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 1319-1327 |
| Seitenumfang | 9 |
| Fachzeitschrift | Soft Computing |
| Jahrgang | 17 |
| Ausgabenummer | 8 |
| Frühes Online-Datum | 6 Feb. 2013 |
| Publikationsstatus | Veröffentlicht - Aug. 2013 |
| Extern publiziert | Ja |
Abstract
In many practical situations, we do not have enough observations to uniquely determine the corresponding probability distribution, we only have enough observations to estimate two parameters of this distribution. In such cases, the traditional statistical approach is to estimate the mean and the standard deviation. Alternatively, we can estimate the two bounds that form the range of the corresponding variable and thus, generate an interval. Which of these two approaches should we select? A natural idea is to select the most informative approach, i.e., an approach in which we need the smallest amount of additional information (in Shannon's sense) to obtain the full information about the situation. In this paper, we follow this idea and come up with the following conclusion: in practical situations in which a 95 % confidence level is sufficient, interval bounds are more informative; however, in situations in which we need higher confidence, the moments approach is more informative.
ASJC Scopus Sachgebiete
- Informatik (insg.)
- Software
- Mathematik (insg.)
- Theoretische Informatik
- Mathematik (insg.)
- Geometrie und Topologie
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in: Soft Computing, Jahrgang 17, Nr. 8, 08.2013, S. 1319-1327.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Interval or moments
T2 - Which carry more information?
AU - Beer, Michael
AU - Kreinovich, Vladik
N1 - Funding Information: This work was partly supported by the National Science Foundation grants HRD-0734825 and DUE-0926721, and by Grant 1 T36 GM078000-01 from the National Institutes of Health. The authors are thankful to all the participants of the Dagstuhl 2011 seminar Uncertainty Modeling and Analysis with Intervals: Foundations, Tools, Applications for valuable discussions, and to the anonymous referees for useful suggestions.
PY - 2013/8
Y1 - 2013/8
N2 - In many practical situations, we do not have enough observations to uniquely determine the corresponding probability distribution, we only have enough observations to estimate two parameters of this distribution. In such cases, the traditional statistical approach is to estimate the mean and the standard deviation. Alternatively, we can estimate the two bounds that form the range of the corresponding variable and thus, generate an interval. Which of these two approaches should we select? A natural idea is to select the most informative approach, i.e., an approach in which we need the smallest amount of additional information (in Shannon's sense) to obtain the full information about the situation. In this paper, we follow this idea and come up with the following conclusion: in practical situations in which a 95 % confidence level is sufficient, interval bounds are more informative; however, in situations in which we need higher confidence, the moments approach is more informative.
AB - In many practical situations, we do not have enough observations to uniquely determine the corresponding probability distribution, we only have enough observations to estimate two parameters of this distribution. In such cases, the traditional statistical approach is to estimate the mean and the standard deviation. Alternatively, we can estimate the two bounds that form the range of the corresponding variable and thus, generate an interval. Which of these two approaches should we select? A natural idea is to select the most informative approach, i.e., an approach in which we need the smallest amount of additional information (in Shannon's sense) to obtain the full information about the situation. In this paper, we follow this idea and come up with the following conclusion: in practical situations in which a 95 % confidence level is sufficient, interval bounds are more informative; however, in situations in which we need higher confidence, the moments approach is more informative.
KW - Information
KW - Intervals
KW - Moments
UR - http://www.scopus.com/inward/record.url?scp=84880776733&partnerID=8YFLogxK
U2 - 10.1007/s00500-013-1002-1
DO - 10.1007/s00500-013-1002-1
M3 - Article
AN - SCOPUS:84880776733
VL - 17
SP - 1319
EP - 1327
JO - Soft Computing
JF - Soft Computing
SN - 1432-7643
IS - 8
ER -