• Communications for Statistical Applications and Methods
• /
• 제7권1호
• /
• pp.291-296
• /
• 2000

Petrov(1996) examined the connection between general moment conditions and the applicability of the strong law lf large numbers to a sequence of pairwise independnt and identically distributed random variables. In this note wee generalize Theorem 1 of Petrov(1996) and also show that still holds under assumption of pairwise negative quadrant dependence(NQD).

• Communications for Statistical Applications and Methods
• /
• 제15권4호
• /
• pp.483-496
• /
• 2008

This paper proposes a class of perturbed symmetric distributions associated with the bivariate elliptically symmetric(or simply bivariate elliptical) distributions. The class is obtained from the nontruncated marginals of the truncated bivariate elliptical distributions. This family of distributions strictly includes some univariate symmetric distributions, but with extra parameters to regulate the perturbation of the symmetry. The moment generating function of a random variable with the distribution is obtained and some properties of the distribution are also studied. These developments are followed by practical examples.

• Journal of the Korean Statistical Society
• /
• 제22권1호
• /
• pp.133-138
• /
• 1993

We consider two estimators of the infection rate in the simple stochastic epidemic model. It is shown that the maximum likelihood estimator of teh infection rate under the discrete time observation does not have the moment of any positive order. Some properties of the Choi-Severo estimator, an approximation to the maximum likelihood estimator, are also investigated.

• Journal of the Korean Statistical Society
• /
• 제5권2호
• /
• pp.101-107
• /
• 1976

One of the important properties of a 'good' response surface design is that the design should be insensitive to wild observations. In this note, a measure of sensitivity to wild observations is studied. It is shown that designs are made robust to wild observations by making $Tr[X'X)^{-1}M]$ small where M is a moment matrix over some region of interest. The proposed criterion is compared with that suggested by Box and Draper. Some about robust two-variable response surface designs are given.

• 한국운동역학회지
• /
• 제28권4호
• /
• pp.227-236
• /
• 2018

Objective: The purpose of this study was to investigate the effects of a 12-week combined exercise program on gait parameters in elderly women with osteoarthritis. Method: The subjects of this study were 11 elderly women (age: $67.09{\pm}2.47$, height: $157.35{\pm}4.30cm$, weight: $62.49{\pm}6.36kg$) with knee osteoarthritis. The combined exercise program of this study was divided into aerobic exercise and lower extremity strengthening exercises. The exercises were performed for 60 minutes per session, three times a week, for a total of 12 weeks. The maximum joint moments of the hip, knee, and ankle joints with walking were obtained with 8-3D cameras (MX-T20, Vicon, USA) and 2-force plate (AMTI OR6-7-400, AMTI, USA). SPSS Windows version 23.0 was used for statistical analysis. A paired t-test was used for pre-post comparison. An alpha level of .05 was utilized in all tests. Results: The maximum extension moment was significantly higher in the hip joint after P1 on the X axis. The maximum joint moment of P3 in extension was statistically significantly lower after intervention. On the Z axis, the maximum joint moment was significantly lower after the exercise intervention at P3. There was a statistically significant increase in the extension moment of the left and right knee joints in the X axis after exercise intervention. In the right ankle joint, P1 (plantar flexion moment) showed a statistically significant high moment after exercise intervention. Conclusion: These results suggest that combined exercise, including lower limb and aerobic exercise, may have a positive effect on mobility and walking moments in patients with osteoarthritis of the knee.

• 한국통계학회:학술대회논문집
• /
• 한국통계학회 2004년도 학술발표논문집
• /
• pp.295-300
• /
• 2004

We consider a G/M/1 queue with two-stage service policy. The server starts to serve with rate of ${\mu}1$ customers per unit time until the number of customers in the system reaches A. At this moment, the service rate is changed to that of ${\mu}2$ customers per unit time and this rate continues until the system is empty. We obtain the stationary distribution of the number of customers in the system.

• 한국소음진동공학회:학술대회논문집
• /
• 한국소음진동공학회 2014년도 추계학술대회 논문집
• /
• pp.600-601
• /
• 2014

• 한국정밀공학회:학술대회논문집
• /
• 한국정밀공학회 2005년도 춘계학술대회 논문집
• /
• pp.602-606
• /
• 2005

A systematic procedure of probability analysis for general distributions is developed based on the first four moments estimated from polynomial interpolation of the system response function and the Pearson system. The function approximation is based on a specially selected experimental region for accuracy and the number of function evaluations is taken equal to that of the unknown coefficient for efficiency. For this purpose, three error-minimizing conditions are proposed and corresponding canonical experimental regions are formed for popular probability. This approach is applied to study the stochastic properties of the performance functions of a MEMS structure, which has quite large fabrication errors compared to other structures. Especially, the vibratory micro-gyroscope is studied using the statistical moments and probability density function (PDF) of the performance function to be the difference between resonant frequencies corresponding to sensing and driving mode. The results show that it is very sensitive to the fabrication errors and that the types of PDF of each variable also affect the stochastic properties of the performance function although they have same the mean and variance.

• Communications for Statistical Applications and Methods
• /
• 제17권4호
• /
• pp.507-513
• /
• 2010

Let {$X_i,-{\infty}$ < 1 < $\infty$} be a doubly infinite sequence of identically distributed and negatively associated random variables with mean zero and finite variance and {$a_i,\;-{\infty}$ < i < ${\infty}$} be an absolutely summable sequence of real numbers. Define a moving average process as $Y_n={\sum}_{i=-\infty}^{\infty}a_{i+n}X_i$, n $\geq$ 1 and $S_n=Y_1+{\cdots}+Y_n$. In this paper we prove that E|$X_1$|$^rh$($|X_1|^p$) < $\infty$ implies ${\sum}_{n=1}^{\infty}n^{r/p-2-q/p}h(n)E{max_{1{\leq}k{\leq}n}|S_k|-{\epsilon}n^{1/p}}{_+^q}<{\infty}$ and ${\sum}_{n=1}^{\infty}n^{r/p-2}h(n)E{sup_{k{\leq}n}|k^{-1/p}S_k|-{\epsilon}}{_+^q}<{\infty}$ for all ${\epsilon}$ > 0 and all q > 0, where h(x) > 0 (x > 0) is a slowly varying function, 1 ${\leq}$ p < 2 and r > 1 + p/2.

• Smart Structures and Systems
• /
• 제20권2호
• /
• pp.207-217
• /
• 2017

Because of the inevitable uncertainties such as structural parameters, external excitations and measurement noises, the effects of uncertainties should be taken into consideration in structural damage detection. In this paper, two probabilistic structural damage detection approaches are proposed to account for the underlying uncertainties in structural parameters and external excitation. The first approach adopts the statistical moment-based structural damage detection (SMBDD) algorithm together with the sensitivity analysis of the damage vector to the uncertain parameters. The approach takes the advantage of the strength SMBDD, so it is robust to measurement noise. However, it requests the number of measured responses is not less than that of unknown structural parameters. To reduce the number of measurements requested by the SMBDD algorithm, another probabilistic structural damage detection approach is proposed. It is based on the integration of structural damage detection using temporal moments in each time segment of measured response time history with the sensitivity analysis of the damage vector to the uncertain parameters. In both approaches, probability distribution of damage vector is estimated from those of uncertain parameters based on stochastic finite element model updating and probabilistic propagation. By comparing the two probability distribution characteristics for the undamaged and damaged models, probability of damage existence and damage extent at structural element level can be detected. Some numerical examples are used to demonstrate the performances of the two proposed approaches, respectively.