An alternative mathematical foundation for statistics

Acta Applicandae Mathematicae

Volumn 89, Issue 1-3, 2005, Pages 217-249

  Lutz, R ^a   Musio, M ^b  

^a UNIVERSITÉ DE HAUTE ALSACE   (France)

^b UNIVERSITY OF CAGLIARI   (Italy)

Author keywords

Non standard analysis; Probability; Statistics

Indexed keywords

PROBABILITY; STATISTICAL METHODS; STATISTICS; THEOREM PROVING;

FREQUENCY STATISTICS; NON-STANDARD ANALYSIS;

NUMERICAL METHODS;

EID: 33645281136     PISSN: 01678019     EISSN: 15729036     Source Type: Journal    
DOI: 10.1007/s10440-005-9009-y     Document Type: Article

References (16)

1. Callot, J. L.: Trois leçons d'Analyse infinitésimales, In: J. M. Salanskis (ed), le labyrinthe du continu, Springer France, Paris, 1992.
2. de Finetti, B.: Teoria delle Probabilità, Einaudi, 1970.
3. Diener, F. and Diener, M. (eds.): Nonstandard Analysis in Practice, Springer, Berlin Heidelberg New York, 1995.
4. Feller, W.; An Introduction to Probability Theory and Its Applications, Vol. I, II, Wiley Series in Probability, 1968.
5. Lutz, R.: Rêveries Infinitésimales, La Gaz. des math. 34 (1987).
6. Lutz, R.: La Force des Théories Infinitésimales Faibles, In: J. M. Salanskis (ed), le labyrinthe du continu, Springer France, Paris, 1992.
7. Lutz, R. and Albuquerque, L. G.: Modern infinitesimals as tools to mach intuitive and formal reasonning in analysis, Synthese 134 (2003), 1-2.
8. Lutz, R. and Goze, M.: Nonstandard analysis: A practical guide with applications, Springer, Lect. Notes Math. 881 (1981).
9. Musio, M.: Linking Statistics and Probability: An Intermediate Theory, Preprint Université de Haute Alsace, 2003.
10. Musio, M. and Lutz, R.: A finitisation of the finitely additive probability theory using non standard analysis, Rend. Accad. Naz. Sci. Detta XL, 112, XVIII, I, (1994), 117-132.
11. Nelson, E.: Internal set theory, Bull. Am. Math. Soc. 83 (1977), 6.
12. Nelson, E.: Radically Elementary Probability Theory, Ann. Math. Studies 117, Princeton U.P., New Jersey., 1987.
13. Peraire, Y.: Théorie Relative des Ensemble Internes, Osaka J. Math. 29 (1995), 2.
14. Robinson, A.: Non-Standard Analysis, North-Holland, Amsterdam, 1966.
15. Salanskis, J. M.: Le Constructivisme Non Standard, Presses Universitaires du Septentrion coll, Histoire des Sciences, Lille, 1999.
16. Van den Berg, I.: Non-Standard Asymptotic Analysis, Lecture notes in Math. no. 1249, Springer, 1987.