• 한국지능시스템학회:학술대회논문집
• /
• 한국퍼지및지능시스템학회 2004년도 춘계학술대회 학술발표 논문집 제14권 제1호
• /
• pp.385-388
• /
• 2004

The present paper establish the improved version of central limit theorem for sums of level-continuous fuzzy random variables as a generalization of central limit theorem for sums of independent and identically distributed random sets.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제29권1호
• /
• pp.31-35
• /
• 2022

In the note, by virtue of Abel's theorem and Abel's limit theorem in the theory of power series, the author provides three proofs for a sum of an alternating series involving central binomial numbers.

• 대한수학회지
• /
• 제37권1호
• /
• pp.1-19
• /
• 2000

We formulate a non-central limit theorem for non-linear functionals of stationary Gaussian vector processes with dependence.

• 대한수학회논문집
• /
• 제29권2호
• /
• pp.351-358
• /
• 2014

In this paper, under some suitable integrability and smoothness conditions on f, we establish the central limit theorems for $$\sum_{k{\leq}N}k^{-1}f(S_k/{\sigma}\sqrt{k})$$, where $S_k$ is the partial sums of strictly stationary mixing random variables with $EX_1=0$ and ${\sigma}^2=EX^2_1+2\sum_{k=1}^{\infty}EX_1X_{1+k}$. We also establish an almost sure limit behaviors of the above sums.

• 대한수학회지
• /
• 제51권1호
• /
• pp.1-15
• /
• 2014

A conditional version of the classical central limit theorem is derived rigorously by using conditional characteristic functions, and a more general version of conditional central limit theorem for the case of conditionally independent but not necessarily conditionally identically distributed random variables is established. These are done anticipating that the field of conditional limit theory will prove to be of significant applicability.

• Journal of the Korean Statistical Society
• /
• 제26권2호
• /
• pp.231-243
• /
• 1997

In this paper we investigate weak convergence of the intergral processes whose index set is the non-compact infinite time interval. Our first goal is to develop the empirical central limit theorem as random elements of [0, .infty.) for an integral process which is constructed from iid variables. In developing the weak convergence as random elements of D[0, .infty.), we will use a result of Ossiander(4) whose proof heavily depends on the total boundedness of the index set. Our next goal is to establish the empirical central limit theorem for the Kaplan-Meier integral process as random elements of D[0, .infty.). In achieving the the goal, we will use the above iid result, a representation of State(6) on the Kaplan-Meier integral, and a lemma on the uniform order of convergence. The first result, in some sense, generalizes the result of empirical central limit therem of Pollard(5) where the process is regarded as random elements of D[-.infty., .infty.] and the sample paths of limiting Gaussian process may jump. The second result generalizes the first result to random censorship model. The later also generalizes one dimensional central limit theorem of Stute(6) to a process version. These results may be used in the nonparametric statistical inference.

• Communications for Statistical Applications and Methods
• /
• 제2권2호
• /
• pp.347-349
• /
• 1995

In this paper a central limit theorem on $L^P(R)$ for $1{\leq}p<{\infty}$ is obtained with an example when ${X_n}$ is a sequence of independent, identically distributed random variables on $L^P(R)$.

• 대한수학회논문집
• /
• 제10권4호
• /
• pp.963-974
• /
• 1995

We formulate central limit theorems for non-linear functionals of stationary Gaussian vector processes with long-range dependence.

• 대한수학회논문집
• /
• 제14권3호
• /
• pp.627-633
• /
• 1999

Let the given distribution $\pi$ have a log-concave density which is proportional to exp(-V(x)) on $R^d$. We consider a Markov chain induced by the method Gibbs sampling having $\pi$ as its in-variant distribution and prove geometric ergodicity and the functional central limit theorem for the process.

• Korean Journal of Mathematics
• /
• 제6권2호
• /
• pp.231-242
• /
• 1998

On the basis of Heyer and Zeuner's results we will treat the central limit theorem for probability measures on hypergroup.