A strong law of large numbers in credibility theory∗
نویسندگان
چکیده
In this paper, the issue of the law of large numbers for fuzzy variables is considered. Since in credibility theory convergence in credibility implies convergence almost sure, the strong law of large numbers is defined via convergence in credibility, while the weak law of large numbers is defined through convergence almost sure. Based on the convergence results about the unform integrability of fuzzy variables, a sufficient condition of the strong law of large numbers for a class of fuzzy variables with unbounded supports is established.
منابع مشابه
MARCINKIEWICZ-TYPE STRONG LAW OF LARGE NUMBERS FOR DOUBLE ARRAYS OF NEGATIVELY DEPENDENT RANDOM VARIABLES
In the following work we present a proof for the strong law of large numbers for pairwise negatively dependent random variables which relaxes the usual assumption of pairwise independence. Let be a double sequence of pairwise negatively dependent random variables. If for all non-negative real numbers t and , for 1 < p < 2, then we prove that (1). In addition, it also converges to 0 in ....
متن کاملA PRELUDE TO THE THEORY OF RANDOM WALKS IN RANDOM ENVIRONMENTS
A random walk on a lattice is one of the most fundamental models in probability theory. When the random walk is inhomogenous and its inhomogeniety comes from an ergodic stationary process, the walk is called a random walk in a random environment (RWRE). The basic questions such as the law of large numbers (LLN), the central limit theorem (CLT), and the large deviation principle (LDP) are ...
متن کاملA Note on the Strong Law of Large Numbers
Petrov (1996) proved the connection between general moment conditions and the applicability of the strong law of large numbers to a sequence of pairwise independent and identically distributed random variables. This note examines this connection to a sequence of pairwise negative quadrant dependent (NQD) and identically distributed random variables. As a consequence of the main theorem ...
متن کاملCREDIBILITY THEORY ORIENTED PREFERENCE INDEX FOR RANKING FUZZY NUMBERS
This paper suggests a novel approach for ranking the most applicable fuzzy numbers, i.e. $LR$-fuzzy numbers. Applying the $alpha$-optimistic values of a fuzzy number, a preference criterion is proposed for ranking fuzzy numbers using the Credibility index. The main properties of the proposed preference criterion are also studied. Moreover, the proposed method is applied for ranking fuzz...
متن کاملLaws of Large Numbers for Random Linear
The computational solution of large scale linear programming problems contains various difficulties. One of the difficulties is to ensure numerical stability. There is another difficulty of a different nature, namely the original data, contains errors as well. In this paper, we show that the effect of the random errors in the original data has a diminishing tendency for the optimal value as the...
متن کامل