pteran.blogspot.com
Pedro Terán's research work: Laws of large numbers without additivity
http://pteran.blogspot.com/2013/03/laws-of-large-numbers-without-additivity.html
Pedro Terán's research work. Still totally `Under construction'. Monday, 18 March 2013. Laws of large numbers without additivity. P Terán (2014). Transactions of the American Mathematical Society. Many results of this kind have been published in the last years, with very heterogenous assumptions. This seems to be the first result where no extra assumption is placed on the random variables (beyond integrability, of course). Converge almost surely to 0. Have `probability' 0 of being smaller than 1. When yo...
pteran.blogspot.com
Pedro Terán's research work: Probabilistic foundations for measurement modelling with fuzzy random variables
http://pteran.blogspot.com/2009/04/probabilistic-foundations-for.html
Pedro Terán's research work. Still totally `Under construction'. Monday, 20 April 2009. Probabilistic foundations for measurement modelling with fuzzy random variables. P Terán (2007). Fuzzy Sets and Systems. For some reason, I never wrote an entry for this paper when I started this blog. It appeared in the FSS special issue Selected papers from IFSA 2005, 11th World Congress of International Fuzzy Systems Association. The paper points out a lot of things that remain to be done. This research was nic...
pteran.blogspot.com
Pedro Terán's research work: A law of large numbers for the possibilistic mean value
http://pteran.blogspot.com/2013/10/a-law-of-large-numbers-for.html
Pedro Terán's research work. Still totally `Under construction'. Thursday, 24 October 2013. A law of large numbers for the possibilistic mean value. P Terán (2014). Fuzzy Sets and Systems. This paper has an interesting idea, I think. In general, random variables in a possibility (instead of probability) space do not satisfy a law of large numbers exactly like the one in probability theory. The reason is that, if the variable takes on at least two different values x. The interesting idea is the following:.
pteran.blogspot.com
Pedro Terán's research work: On convergence in necessity and its laws of large numbers
http://pteran.blogspot.com/2008/05/on-convergence-in-necessity-and-its.html
Pedro Terán's research work. Still totally `Under construction'. Wednesday, 7 May 2008. On convergence in necessity and its laws of large numbers. P Terán (2008). In: Soft Methods for Handling Variability and Imprecision. 289- 296. Springer, Berlin. Proceedings of the 4th Intl. Conf. on Soft Methods in Statistics and Probability]. This paper presents some convergence results, in an attempt to clarify the difference between LLNs for possibilistic variables and LLNs for their distributions. It also shows t...
pteran.blogspot.com
Pedro Terán's research work: Centrality as a gradual notion: A new bridge between fuzzy sets and statistics
http://pteran.blogspot.com/2013/03/centrality-as-gradual-notion-new-bridge.html
Pedro Terán's research work. Still totally `Under construction'. Monday, 18 March 2013. Centrality as a gradual notion: A new bridge between fuzzy sets and statistics. P Terán (2011). International Journal of Approximate Reasoning. According to one point of view, fuzzy set theoretical notions are problematic unless they can be justified as / explained from / reduced to ordinary statistics and probability. I can't say that this makes much sense to me. A fuzzy set of central points. From the paper's abstra...
pteran.blogspot.com
Pedro Terán's research work: Counterexamples to a Central Limit Theorem and a Weak Law of Large Numbers for capacities
http://pteran.blogspot.com/2014/11/counterexamples-to-central-limit.html
Pedro Terán's research work. Still totally `Under construction'. Saturday, 8 November 2014. Counterexamples to a Central Limit Theorem and a Weak Law of Large Numbers for capacities. P Terán (2015). Statistics and Probability Letters. This note shows that the main results in a former SPL. At which point I felt so deeply offended by the argument of authority that I just cut all communication. 183; Laws of large numbers without additivity. 183; Non-additive probabilities and the laws of large numbers.
pteran.blogspot.com
Pedro Terán's research work: Strong law of large numbers for t-normed arithmetics
http://pteran.blogspot.com/2007/11/strong-law-of-large-numbers-for-t.html
Pedro Terán's research work. Still totally `Under construction'. Tuesday, 13 November 2007. Strong law of large numbers for t-normed arithmetics. P Terán (2008). Fuzzy Sets and Systems. This paper was conceived and written in late 2001 and early 2002. For years, I stubbornly tried to have it published in a Statistics and Probability journal. A tale of this epic yet unfruitful quest was told in my personal blog. I finally quit and submitted it to FSS. Where I knew knowledgeable reviewers would be used.
pteran.blogspot.com
Pedro Terán's research work: Connections between statistical depth functions and fuzzy sets
http://pteran.blogspot.com/2010/09/connections-between-statistical-depth.html
Pedro Terán's research work. Still totally `Under construction'. Thursday, 23 September 2010. Connections between statistical depth functions and fuzzy sets. P Terán (2010). In: Combining Soft Computing and Statistical Methods in Data Analysis. CBorgelt et al., editors), 611- 618. Springer, Berlin. Proceedings of the 5th Intl. Conf. on Soft Methods in Statistics and Probability]. Invited session Probabilistic aspects of fuzzy sets. Subsequent work will be typed somewhere in time. Pedro Terán recieved his...
pteran.blogspot.com
Pedro Terán's research work: On the equivalence of Aumann and Herer expectations of random sets
http://pteran.blogspot.com/2009/04/on-equivalence-of-aumann-and-herer.html
Pedro Terán's research work. Still totally `Under construction'. Tuesday, 7 April 2009. On the equivalence of Aumann and Herer expectations of random sets. P Terán (2008). Test. Trying to understand when the Herer expectation of a random set falls into the abstract definition of expectation in A law of large numbers in a metric space with a convex combination operation. Unexpectedly triggered a line of research on the Herer expectation itself. As you can read here. To download, click on the title or here.
