• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 1998.10a
• /
• pp.9-15
• /
• 1998

In this paper, we introduce new results of law large numbers for mutually T-related fuzzy numbers, when T is Archimedean t-norm and spreads are random variables, and generalize earlier result of Fullr[FSS 45(1992) 299-303].

• Honam Mathematical Journal
• /
• v.30 no.3
• /
• pp.479-486
• /
• 2008

Let {${\Omega}$, F, P} be a probability space and {$X_n{\mid}n{\geq}1$} be a sequence of random variables defined on it. We study the Hajeck-Renyi-type inequality for p..mixing random variable sequences and obtain the strong law of large numbers by using this inequality. We also consider the strong law of large numbers for weighted sums of ${\tilde{\rho}}$-mixing sequences.

• Bulletin of the Korean Mathematical Society
• /
• v.36 no.2
• /
• pp.273-285
• /
• 1999

In this paper we establish the weak law of large numbers for randomly weighted partial sums of random variables and study conditions imposed on the triangular array of random weights {$W_{nj}{\;}:{\;}1{\leq}j{\leq}n,{\;}n{\geq}1$} and on the triangular array of random variables {$X_{nj}{\;}:{\;}1{\leq}j{\leq}n,{\;}{\geq}1$} which ensure that $\sum_{j=1}^{n}{\;}W_{nj}{\mid}X_{nj}{\;}-{\;}B_{nj}{\mid}$ converges In probability to 0, where {$B_{nj}{\;}:{\;}1{\;}{\leq}{\;}j{\;}{\leq}{\;}n,{\;}n{\;}{\geq}{\;}1$} is a centering array of constants or random variables.

• Honam Mathematical Journal
• /
• v.34 no.2
• /
• pp.209-217
• /
• 2012

Convergence rates in the law of large numbers for i.i.d. random variables have been generalized by Gut[Gut, A., 1978. Marc inkiewicz laws and convergence rates in the law of large numbers for random variables with multidimensional indices, Ann. Probab. 6, 469-482] to random fields with all indices having the same power in the normalization. In this paper we generalize these convergence rates to the identically distributed and negatively associated random fields with different indices having different power in the normalization.

• Bulletin of the Korean Mathematical Society
• /
• v.35 no.4
• /
• pp.709-718
• /
• 1998

In this paper we obtain strong laws of large numbers for 2-dimensional arrays of random variables which are either pairwise positive quadrant dependent or associated. Our results imply extensions of Etemadi`s strong laws of large numbers for nonnegative random variables to the 2-dimensional case.

• Journal of the Korean Mathematical Society
• /
• v.47 no.5
• /
• pp.1055-1075
• /
• 2010

In presented paper there were studied some properties of Benford's law. The existence of this law in not necessary large sets of numbers is a very interesting example that can show how the complex phenomena can appear in the positional number systems. Such systems seem to be very simple and intuitive and help us proceed with numbers. However, their simplicity in the case of usage in our lifetime is not necessary connected with the simplicity in the case of laws that govern them. Even if this laws indicate the existence of self-similar properties.

• Communications for Statistical Applications and Methods
• /
• v.9 no.2
• /
• pp.451-457
• /
• 2002

We derive the strong laws of large numbers for weighted averages of partial sums of random variables which are either associated or negatively associated. Our theorems extend and generalize strong law of large numbers for weighted sums of associated and negatively associated random variables of Matula(1996; Probab. Math. Statist. 16) and some results in Birkel(1989; Statist. Probab. Lett. 7) and Matula (1992; Statist. Probab. Lett. 15 ).

• Journal of the Korean Statistical Society
• /
• v.33 no.1
• /
• pp.99-106
• /
• 2004

Let {X, $X_{n}, n\;{\geq}\;1$} be a sequence of identically distributed, negatively associated (NA) random variables and assume that $│X│^{r}$, r > 0, has a finite moment generating function. A strong law of large numbers is established for weighted sums of these variables.

• Journal of the Korean Mathematical Society
• /
• v.45 no.4
• /
• pp.1101-1111
• /
• 2008

Under the condition of h-integrability and appropriate conditions on the array of weights, we establish complete convergence and strong law of large numbers for weighted sums of an array of dependent random variables.

• Journal of the Korean Mathematical Society
• /
• v.49 no.2
• /
• pp.235-249
• /
• 2012

In the paper by Liu and Lin (Statist. Probab. Lett. 76 (2006), no. 16, 1787-1799), a new kind of precise asymptotics in the law of large numbers for the sequence of i.i.d. random variables, which includes complete convergence as a special case, was studied. This paper is devoted to the study of this new kind of precise asymptotics in the law of large numbers for moving average process under $\phi$-mixing assumption and some results of Liu and Lin [6] are extended to such moving average process.