• Communications of the Korean Mathematical Society
• /
• v.17 no.3
• /
• pp.535-540
• /
• 2002

Let X$_1$, X$_2$‥‥,X$\_$n/ be n independent and identically distributed random variables with continuous cumulative distribution function F(x). Let us rearrange the X's in the increasing order X$\_$1:n/ $\leq$ X$\_$2:n/ $\leq$ ‥‥ $\leq$ X$\_$n:n/. We call X$\_$k:n/ the k-th order statistic. Then X$\_$n:n/ - X$\_$n-1:n/ and X$\_$n-1:n/ are independent if and only if f(x) = 1-e(equation omitted) with some c > 0. And X$\_$j/ is an upper record value of this sequence lf X$\_$j/ > max(X$_1$, X$_2$,¨¨ ,X$\_$j-1/). We define u(n) = min(j|j > u(n-1),X$\_$j/ > X$\_$u(n-1)/, n $\geq$ 2) with u(1) = 1. Then F(x) = 1 - e(equation omitted), x > 0 if and only if E[X$\_$u(n+3)/ - X$\_$u(n)/ | X$\_$u(m)/ = y] = 3c, or E[X$\_$u(n+4)/ - X$\_$u(n)/|X$\_$u(m)/ = y] = 4c, n m+1.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.9 no.2
• /
• pp.91-97
• /
• 2005

If ${\beta}\;>\;1$, then every non-negative number x has a ${\beta}-expansion$, i.e., $$x\;=\;{\epsilon}_0(x)\;+\;{\frac{\epsilon_1(x)}{\beta}}\;+\;{\frac{\epsilon_2(x)}{\beta}}\;+\;{\cdots}$$ where ${\epsilon}_0(x)\;=\;[x],\;{\epsilon}_1(x)\;=\;[\beta(x)],\;{\epsilon}_2(x)\;=\;[\beta(({\beta}x))]$, and so on ([x] denotes the integral part and (x) the fractional part of the real number x). Let T be a transformation on [0,1) defined by $x\;{\rightarrow}\;({\beta}x)$. It is well known that the relative frequency of $k\;{\in}\;\{0,\;1,\;{\cdots},\;[\beta]\}$ in ${\beta}-expansion$ of x is described by the T-invariant absolutely continuous measure ${\mu}_{\beta}$. In this paper, we show the mod M normality of the sequence $\{{\in}_n(x)\}$.

• Journal of the Chungcheong Mathematical Society
• /
• v.27 no.2
• /
• pp.157-163
• /
• 2014

Let {$X_i$, $1{\leq}i{\leq}n$} be a sequence of i.i.d. sequence of positive random variables with common absolutely continuous cumulative distribution function F(x) and probability density function f(x) and $E(X^2)$ < ${\infty}$. The random variables X + Y and $\frac{(X-Y)^2}{(X+Y)^2}$ are independent if and only if X and Y have gamma distributions. In addition, the random variables $S_n$ and $\frac{\sum_{i=1}^{m}(X_i)^2}{(S_n)^2}$ with $S_n=\sum_{i=1}^{n}X_i$ are independent for $1{\leq}m$ < n if and only if $X_i$ has gamma distribution for $i=1,{\cdots},n$.

• Communications for Statistical Applications and Methods
• /
• v.18 no.4
• /
• pp.485-493
• /
• 2011

The proportional likelihood ratio order is an extension of the likelihood ratio order for the non-negative absolutely continuous random variables. In addition, the Lindley distribution has been over looked as a mixture of two exponential distributions due to the popularity of the exponential distribution. In this paper, we first recalled the above concepts and then obtained various properties of the Lindley distribution due to the proportional likelihood ratio order. These results are more general than the likelihood ratio ordering aspects related to this distribution. Finally, we discussed the proportional likelihood ratio ordering in view of the weighted version of the Lindley distribution.

• Communications for Statistical Applications and Methods
• /
• v.17 no.4
• /
• pp.493-505
• /
• 2010

Developing a test for independence of random variables X and Y against the alternative has an important role in statistical inference. Kochar and Gupta (1987) proposed a class of tests in view of Block and Basu (1974) model and compared the powers for sample sizes n = 8, 12. In this paper, we evaluate Kochar and Gupta (1987) class of tests for testing independence against quadrant dependence in absolutely continuous bivariate Farlie-Gambel-Morgenstern distribution, via a simulation study for sample sizes n = 6, 8, 10, 12, 16 and 20. Furthermore, we compare the power of the tests with that proposed by G$\ddot{u}$uven and Kotz (2008) based on the asymptotic distribution of the test statistics.

• Journal of the Korean Mathematical Society
• /
• v.54 no.6
• /
• pp.1879-1903
• /
• 2017

In this paper we study the closure property and probability tail asymptotics for randomly weighted sums $S^{\Theta}_n={\Theta}_1X_1+{\cdots}+{\Theta}_nX_n$ for long-tailed random variables $X_1,{\ldots},X_n$ and positive bounded random weights ${\Theta}_1,{\ldots},{\Theta}_n$ under similar dependence structure as in [26]. In particular, we study the case where the distribution of random vector ($X_1,{\ldots},X_n$) is generated by an absolutely continuous copula.

• The Journal of the Acoustical Society of Korea
• /
• v.17 no.4E
• /
• pp.11-16
• /
• 1998

For large vocabulary speech recognition using HMMs, context-dependent subword units have been often employed. However, when context-dependent phone models are used, they result in a system which has too may parameters to train. The problem of too many parameters and too little training data is absolutely crucial in the design of a statistical speech recognizer. Furthermore, when building large vocabulary speech recognition systems, unseen triphone problem is unavoidable. In this paper, we propose the modified phonetic decision tree algorithm for the automatic prediction of unseen triphones which has advantages solving these problems through following two experiments in Japanese contexts. The baseline experimental results show that the modified tree based clustering algorithm is effective for clustering and reducing the number of states without any degradation in performance. The task experimental results show that our proposed algorithm also has the advantage of providing a automatic prediction of unseen triphones.

• Journal of the Chungcheong Mathematical Society
• /
• v.24 no.1
• /
• pp.85-89
• /
• 2011

We present characterizations of the Pareto distribution by the independent property of upper record values in such a way that F(x) has a Pareto distribution if and only if $\frac{X_{U(n)}}{X_{U(m)}}$ and $X_{U(m)}$ are independent for $1{\leq}m. Futhermore, the characterizations should find that F(x) has a Pareto distribution if and only if $\frac{X_{U(n)}}{X_{U(n)}{\pm}X_{U(m)}}$ and $X_{U(m)}$ are independent for $1{\leq}m.

• Journal of the Korean BIBLIA Society for library and Information Science
• /
• v.28 no.4
• /
• pp.203-221
• /
• 2017

This study is to suggest some improvement directions of the criteria for the management evaluation in order to contribute to the achievement of lasting value of the continuous development and publicity in regard to the public library means-efficiency. To this end, This study analyzed the means-efficiency evaluation criteria via theoretical review on business analysis of private enterprise and the analysis framework based on it. The improvement of evaluation criteria in regard to efficiency for the continuous development of public library are as follows. 1) Regardless of domestic and foreign, an efficiency index in the performance evaluation index of public library is absolutely insufficient. The sufficient indexes measuring efficiency which is appropriate for the concept of performance should be developed. 2) A flow data representing input and performance in certain time period is insufficient. Therefore, evaluation index consisted of flow data should be more developed. 3) Long term stock data is excluded in the term cost as it is the cost used for the long term such as fixed assets. However, it is useful as input data, which is realized through the perfect accounting.

• Proceedings of the KIPE Conference
• /
• 2013.11a
• /
• pp.63-64
• /
• 2013

Induction motors' faults detection is almost a popular topic among researchers. Monitoring the output of motors is a key factor in detecting these faults. (Short-time) Fourier, (continuous, discrete) wavelet, and extended Park vector transformations are among the methods for fault detection. One major deficiency of these methods is not being able to detect the severity of faults that carry low energy information, e.g. in ball bearing system failure, there is absolutely no way to detect the severity of fault using Fourier or wavelet transformations. In this paper, the authors have applied the Discrete Wavelet Transform (DWT) frequency-domain analysis to detect bearing faults in an induction motor. In other words, in discrete transform which the output signal is decomposed in several steps and frequency resolution increases considerably, the frequency-band analysis is performed and it will be verified that first of all, fault sidebands become more recognizable for detection in higher levels of decomposition, and secondly, the inner race bearing faults turn out easier in these levels; and all these matter because of eliminating the not-required high energy components in lower levels of decomposing.