• 응용통계연구
• /
• 제22권1호
• /
• pp.205-220
• /
• 2009

For modeling skewed semicircular data, we derive new family of the exponential distributions. We extend it to the l-axial exponential distribution by a transformation for modeling any arc of arbitrary length. It is straightforward to generate samples from the f-axial exponential distribution. Asymptotic result reveals two things. The first is that linear exponential distribution can be used to approximate the l-axial exponential distribution. The second is that the l-axial exponential distribution has the asymptotic memoryless property though it doesn't have strict memoryless property. Some trigonometric moments are also derived in closed forms. Maximum likelihood estimation is adopted to estimate model parameters. Some hypotheses tests and confidence intervals are also developed. The Kolmogorov-Smirnov test is adopted for goodness of fit test of the l-axial exponential distribution. We finally obtain a bivariate version of two kinds of the l-axial exponential distributions.

• 대한수학회보
• /
• 제59권4호
• /
• pp.979-991
• /
• 2022

A special class of exponential dispersion models is the class of Tweedie distributions. This class is very significant in statistical modeling as it includes a number of familiar distributions such as Gaussian, Gamma and compound Poisson. A Tweedie distribution has a power parameter p, a mean m and a dispersion parameter 𝜙. The value of the power parameter lies in identifying the corresponding distribution of the Tweedie family. The basic objective of this research work resides in investigating the existence of the implicit estimator of the power parameter of the Tweedie distribution. A necessary and sufficient condition on the mean parameter m, suggesting that the implicit estimator of the power parameter p exists, was established and we provided some asymptotic properties of this estimator.

• 응용통계연구
• /
• 제26권5호
• /
• pp.759-766
• /
• 2013

본 논문에서는 두꺼운 꼬리를 갖는 확률분포들의 여러 부류에 대해서 살펴본다. 주어진 하나의 확률분포가 이들 중 어떤 부류에 속하는 지를 알려면 해당 분포의 꼬리 확률에 대한 (점근) 표현식을 알아야만 한다. 그러나 대다수의 절대 연속 확률분포들은 분포함수가 아닌 확률밀도함수로 명시되기 때문에 통상적으로 이들의 꼬리 확률에 대한 표현식을 얻는 작업은 그리 쉬운 일이 아니다. 본 논문에서는 이러한 경우 확률밀도함수만을 이용하여 꼬리 확률에 대한 점근 표현식을 쉽게 얻을 수 있는 하나의 방법을 제안한다. 또한 제안한 방법을 설명하기 위하여 몇가지 예를 첨부한다.

• Journal of the Korean Statistical Society
• /
• 제24권1호
• /
• pp.127-139
• /
• 1995

This paper is concerned with the asymptotic properties of the least absolute deviation estimators for nonlinear regression models. The simple and practical sufficient conditions for the strong consistency and the asymptotic normality of the least absolute deviation estimators are given. It is confirmed that the extension of these properties to wide class of regression functions can be established by imposing some condition on the input values. A confidence region based on the least absolute deviation estimators is proposed and some desirable asymptotic properties including the asymptotic relative efficiency also discussed for various error distributions. Some examples are given to illustrate the application of main results.

• Journal of the Korean Statistical Society
• /
• 제28권4호
• /
• pp.435-441
• /
• 1999

A 'convergence in probability' rate of the empirical distributions and quantiles of linear processes is obtained. As an application of the limit theorems, a trimmed mean for the location of the linear process is considered. It is shown that the trimmed mean is asymptotically normal. A consistent estimator for the asymptotic variance of the trimmed mean is provided.

• Communications for Statistical Applications and Methods
• /
• 제8권1호
• /
• pp.137-145
• /
• 2001

There are many situations in which the well-known tests such as log-rank test and Gehan-Wilcoxon test fail to detect the survival differences. Assuming large samples, these tests are developed asymptotically normal properties. Thus, they shall be called asymptotic tests in this paper, Several asymptotic tests sensitive to some specific types of survival differences have been recently proposed. This paper compares by simulations the test levels and the powers of the conventional asymptotic tests and their random permutation versions. Simulation studies show that the random permutation tests possess competitive powers compared to the corresponding asymptotic tests, keeping exact test levels even in the small sample case. It also provides the guidelines for choosing the valid and most powerful test under the given situation.

• Structural Engineering and Mechanics
• /
• 제49권3호
• /
• pp.355-372
• /
• 2014

Considering the history of severe earthquakes and the presence of active faults in the greater Tehran region, the possibility of a destructive earthquake occurring is high and seismic hazard analysis is crucial. Gumbel distributions are commonly-used statistical distributions in earthquake engineering and seismology. Their main advantage is their basis on the largest earthquake magnitudes selected from an equal-time predefined set. In this study, the first asymptotic distribution of extremes is used to estimate seismicity parameters and peak ground acceleration (PGA). By assuming a Poisson distribution for the earthquakes, after estimation of seismicity parameters, the mean return period and the probable maximum magnitude within a given time interval are obtained. A maximum probable magnitude of 7.0 has a mean return period of 100 years in this region. For a return period of 475 years, the PGA in the greater Tehran region is estimated to be 0.39g to 0.42g, depending on local site conditions. This value is greater than that of the Iranian Code for Seismic Design of Buildings, indicating that a revision of the code is necessary.

• 대한기계학회:학술대회논문집
• /
• 대한기계학회 2004년도 추계학술대회
• /
• pp.1247-1252
• /
• 2004

The present paper is devoted to the modeling method based on an averaging approach for thermal analysis of microchannel heat sinks subjected to the uniform wall temperature condition. Solutions for velocity and temperature distributions are presented using the averaging approach. When the aspect ratio of the microchannel is higher than 1, these solutions accurately evaluate thermal resistances of heat sinks. Asymptotic solutions for velocity and temperature distributions at the high-aspect-ratio limit are alsopresented by using the scale analysis. Asymptotic solutions are simple, but shown to predict thermal resistances accurately when the aspect ratio is higher than 10. The effects of the aspect ratio and the porosity on the friction factor and the Nusselt number are presented. Characteristics of the thermal resistance of microchannel heat sinks are also discussed.

• 품질경영학회지
• /
• 제23권4호
• /
• pp.157-166
• /
• 1995

Process capability indices are used to determine whether a production process is capable of producing items within a specified tolerance. We could estimate the finite sample distributions of some process capability indices with bootstrap method. In this paper, we derive the asymptotic bootstrap distributions of some process capability indices ${\hat{C}}^*_p$, ${\hat{C}}^*_{pk}$ and ${\hat{C}}^*_{pm}$ under general proper conditions. These asymptotic distributiops would be used in constructing some bootstrap confidence intervals. Also, we examine some small sample properties related to these estimators by some simulations.

• 한국경영과학회지
• /
• 제28권4호
• /
• pp.145-153
• /
• 2003

In this Paper, we examine the limiting distributional behaviour of extreme values of mixed Erlang random variables. We show that, in the finite mixture of Erlang distributions, the component distribution with an asymptotically dominant tail has a critical effect on the asymptotic extreme behavior of the mixture distribution and it converges to the Gumbel extreme-value distribution. Normalizing constants are also established. We apply this result to characterize the asymptotic distribution of maxima of sojourn times in M/M/s queuing system. We also show that Erlang mixtures with continuous mixing may converge to the Gumbel or Type II extreme-value distribution depending on their mixing distributions, considering two special cases of uniform mixing and exponential mixing.