| Title:
|
Null events and stochastical independence (English) |
| Author:
|
Colleti, Giulianella |
| Author:
|
Scozzafava, Romano |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
34 |
| Issue:
|
1 |
| Year:
|
1998 |
| Pages:
|
[69]-78 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we point out the lack of the classical definitions of stochastical independence (particularly with respect to events of 0 and 1 probability) and then we propose a definition that agrees with all the classical ones when the probabilities of the relevant events are both different from 0 and 1, but that is able to focus the actual stochastical independence also in these extreme cases. Therefore this definition avoids inconsistencies such as the possibility that an event $A$ can be at the same time stochastically independent and logically dependent on an event $B$. In a forthcoming paper we will deepen (in this context) the concept of conditional independence (which is just sketched in the last section of the present paper) and we will deal also with the extension of these results to the general case of any (finite) number of events. (English) |
| Keyword:
|
stochastic independence |
| Keyword:
|
conditional independence |
| MSC:
|
03B48 |
| MSC:
|
60A05 |
| MSC:
|
60A99 |
| idZBL:
|
Zbl 1274.03040 |
| idMR:
|
MR1619056 |
| . |
| Date available:
|
2009-09-24T19:13:47Z |
| Last updated:
|
2015-03-27 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135186 |
| . |
| Reference:
|
[1] Coletti G., Scozzafava R.: Characterization of coherent conditional probabilities as a tool for their assessment and extension.Internat. J. Uncertainty, Fuzziness and Knowledge–Based Systems 4 (1996), 103–127 Zbl 1232.03010, MR 1390898, 10.1142/S021848859600007X |
| Reference:
|
[2] Coletti G., Scozzafava R.: Exploiting zero probabilities.In: Proceedings EUFIT ’97, ELITE Foundation, Aachen, 1997, pp. 1499–1503 |
| Reference:
|
[3] Finetti B. de: Les probabilité nulles.Bull. Sci. Math. 60 (1936), 275–288 |
| Reference:
|
[4] Scozzafava R.: A survey of some common misunderstandings concerning the role and meaning of finitely additive probabilities in statistical inference.Statistica 44 (1984), 21–45 Zbl 0557.62004, MR 0766688 |
| . |
