• Journal of the Korean Statistical Society
• /
• 제13권1호
• /
• pp.1-19
• /
• 1984

A random effects model of a one-way layout contingency table is developed using a Dirichlet-multinomial distribution. A test statistic, say $T_k$, is suggested for detecting Dirichlet-multinomial departure from a multinomial distribution. It is shown that the $T_k$ test is asymptotically superior to the classical chi-square test based on the asymptotic relative efficiency. This superiority is further evidenced by a Monte Carlo simulation.

• Journal of the Korean Data and Information Science Society
• /
• 제18권4호
• /
• pp.1171-1177
• /
• 2007

We consider estimation of the right-tail probability in a log-Laplace random variable, As we derive the density of ratio of two independent log-Laplace random variables, the k-th moment of the ratio is represented by a special mathematical function. and hence variance of the ratio can be represented by a psi-function.

• 충청수학회지
• /
• 제28권2호
• /
• pp.187-194
• /
• 2015

The concept of sub-independence is based on the convolution of the distributions of the random variables. It is much weaker than that of independence, but is shown to be sufficient to yield the conclusions of important theorems and results in probability and statistics. It also provides a measure of dissociation between two random variables which is much stronger than uncorrelatedness. Inspired by the excellent work of Jin and Lee (2014), we present certain characterizations of gamma distribution based on the concept of sub-independence.

• Journal of the Korean Data and Information Science Society
• /
• 제18권3호
• /
• pp.689-696
• /
• 2007

This paper considers a Bayesian approach to determine an optimal PM policy with random maintenance quality. Thus, we assume that the quality of a PM action is a random variable following a probability distribution. When the failure time is Weibull distribution with uncertain parameters, a Bayesian approach is established to formally express and update the uncertain parameters for determining an optimal PM policy. Finally, the numerical examples are presented for illustrative purpose.

• 한국수학교육학회지시리즈A:수학교육
• /
• 제59권1호
• /
• pp.47-62
• /
• 2020

본 연구에서는 이산확률분포 파악에 필요한 지식을 표본공간의 각 원소에 정의된 확률, 이산확률변수의 정의, 이산확률변수에 정의되는 확률, 그리고 이들 사이의 관계에 대한 지식으로 정의하고, 예비수학교사가 해당 지식을 어느 정도 이해하고 있는지에 대하여 살펴보았다. 이를 위해 검사 도구를 개발하고 사범대학생 47명을 대상으로 조사하였다.

• 대한수학회보
• /
• 제34권2호
• /
• pp.295-303
• /
• 1997

Let ${X_k : k = 1, 2, \cdots}$ be a sequence of independent, identically distributed integer-valued random variables with common distribution function F.

• Journal of applied mathematics & informatics
• /
• 제28권1_2호
• /
• pp.515-521
• /
• 2010

In multivariate analysis, the inversion formula of the Stieltjes transform is used to find the density of a spectral distribution of random matrices of sample covariance type. Let $B_n\;=\;\frac{1}{N}Y_nY_n^TT_n$ where $Y_n\;=\;[Y_{ij}]_{n\;{\times}\;N}$ is with independent, identically distributed entries and $T_n$ is an $n\;{\times}\;n$ symmetric non-negative definite random matrix independent of the $Y_{ij}$'s. In the present paper, using the inversion formula of the Stieltjes transform, we will find that the limiting distribution of $B_n$ has a continuous density function away from zero.

• 대한수학회논문집
• /
• 제19권1호
• /
• pp.169-177
• /
• 2004

For a stationary field $\{X_{\b{j}},\b{j}{\;}\in{\;}{\mathbb{Z}}^d_{+}\}$ of associated random variables with distribution function $F(x)\;=\;P(X_{\b{1}}\;{\leq}\;x)$ we study strong consistency and asymptotic normality of the empirical distribution function, which is proposed as an estimator for F(x). We also consider strong consistency and asymptotic normality of the empirical survival function by applying these results.

• 충청수학회지
• /
• 제22권3호
• /
• pp.519-524
• /
• 2009

In multivariate analysis, the inversion formula of the Stieltjes transform is used to find the density of a spectral distribution of random matrices of sample covariance type. Let $B_{n}\;=\;\frac{1}{n}Y_{m}^{T}T_{m}Y_{m}$ where $Ym\;=\;[Y_{ij}]_{m{\times}n}$ is with independent, identically distributed entries and $T_m$ is an $m{\times}m$ symmetric nonnegative definite random matrix independent of the $Y_{ij}{^{\prime}}s$. In the present paper, using the inversion formula of the Stieltjes transform, we will find the density function of the limiting distribution of $B_n$ away from zero.

• Journal of the Korean Statistical Society
• /
• 제33권1호
• /
• pp.107-128
• /
• 2004

Bivariate Laplace distributions for which both marginal distributions and Laplace are discussed. Three kinds of bivariate Laplace distributions which are extended bivariate exponential distributions of Gumbel (1960) are introduced in this paper. These symmetrical distributions are compared with asymmetrical distributions of Kotz et al. (2000). Their probability density functions, cumulative distribution functions are derived. Conditional skewnesses and kurtoses are also defined. Their correlation coefficients are calculated and compared with others. We proposed bivariate random vector generating methods whose distributions are bivariate Laplace. With sample means and medians obtained from generated random vectors, variance and covariance matrices of means and medians are calculated and discussed with those of bivariate normal distribution.