• Communications for Statistical Applications and Methods
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• v.15 no.3
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• pp.325-332
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• 2008

We consider estimation of reliability P(Y < X) and distribution of the ratio when X and Y are independent uniform random variable and power function random variable, respectively and also consider the estimation problem when X and Y are independent uniform random variable and a half-normal random variable, respectively.

• Communications for Statistical Applications and Methods
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• v.20 no.3
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• pp.169-174
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• 2013

The ROC curve is drawn with two conditional cumulative distribution functions (or survival functions) of the univariate random variable. In this work, we consider joint cumulative distribution functions of k random variables, and suggest a ROC curve for multivariate random variables. With regard to the values on the line, which passes through two mean vectors of dichotomous states, a joint cumulative distribution function can be regarded as a function of the univariate variable. After this function is modified to satisfy the properties of the cumulative distribution function, a ROC curve might be derived; moreover, some illustrative examples are demonstrated.

• Structural Engineering and Mechanics
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• v.86 no.3
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• pp.349-359
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• 2023

This paper presents a technique for determining the optimal number of elements in stochastic finite element analysis based on reliability analysis. Using the change-of-variable perturbation stochastic finite element approach, the probability density function of the dynamic responses of stochastic structures is explicitly determined. This method combines the perturbation stochastic finite element method with the change-of-variable technique into a united model. To further examine the relationships between the random fields, discretization of the random field parameters, such as the variance function and the scale of fluctuation, is also performed. Accordingly, the reliability index is calculated based on the explicit probability density function of responses with Gaussian or non-Gaussian random fields in any number of elements corresponding to the random field discretization. The numerical examples illustrate the effectiveness of the proposed method for a one-dimensional cantilever reinforced concrete column and a two-dimensional steel plate shear wall. The benefit of this method is that the probability density function of responses can be obtained explicitly without the use simulation techniques. Any type of random variable with any statistical distribution can be incorporated into the calculations, regardless of the restrictions imposed by the type of statistical distribution of random variables. Consequently, this method can be utilized as a suitable guideline for the efficient implementation of stochastic finite element analysis of structures, regardless of the statistical distribution of random variables.

• Journal of the Korean Data and Information Science Society
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• v.15 no.2
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• pp.405-411
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• 2004

In the analysis of cancer data, it is important to make inferences of survival function and to assess the effects of covariates. Cox's proportional hazard model(PHM) and Beran's nonparametric method are generally used to estimate the survival function with covariates. We adjusted the incomplete survival time using the Buckley and James's(1979) pseudo random variables, and then proposed the estimator for the conditional survival function. Also, we carried out the simulation studies to compare the performances of the proposed method.

• Journal of the Korean Statistical Society
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• v.24 no.2
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• pp.471-479
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• 1995

A random shock model for a linearly deteriorating system is introduced. The system deteriorating linearly with time is subject to random shocks which arrive according to a Poisson process and decrease the state of the system by a random amount. The system is repaired by a repairmen arriving according to another Poisson process if the state when he arrives is below a threshold. Explicit expressions are deduced for the characteristic function of the distribution function of X(t), the state of the system at time t, and for the distribution function of X(t) if X(t) is over the threshold. The stationary case is briefly discussed.

• Journal of the Korean Data and Information Science Society
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• v.18 no.4
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• pp.1171-1177
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• 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.

• Communications of the Korean Mathematical Society
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• v.20 no.3
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• pp.547-562
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• 2005

The distribution of products of random variables is of interest in many areas of the sciences, engineering and medicine. This has increased the need to have available the widest possible range of statistical results on products of random variables. In this note, the distribution of the product | XY | is derived when X and Y are Student's t and Bessel function random variables distributed independently of each other.

• Journal of the Korean Statistical Society
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• v.25 no.1
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• pp.153-159
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• 1996

Sums of independent random variables $S_n = X_1 + X_ + cdots + X_n$ are considered, where the X$_{n}$ are chosen according to a stationary process of distributions. Given the time t .geq. O, let N (t) be the number of indices n for which O < $S_n$ $\geq$ t. In this set up we prove that N (t)/t converges almost surely and in $L^1$ as t longrightarrow $\infty$, which generalizes classical renewal theorem.m.

• Bulletin of the Korean Mathematical Society
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• v.57 no.1
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• pp.51-68
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• 2020

In this paper, the author considers the nonparametric regression model with negatively orthant dependent random variables. The wavelet procedures are developed to estimate the regression function. For the wavelet estimator of unknown function g(·), the almost sure consistency is derived and the complete consistency is established under the mild conditions. Our results generalize and improve some known ones for independent random variables and dependent random variables.

• International Journal of Aeronautical and Space Sciences
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• v.15 no.3
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• pp.302-308
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• 2014

In this paper, a detailed investigation of the random vibration test is presented for strapdown inertial navigation systems (INS). The effect of the random vibration test has been studied from the point of view of navigation performance. The role of distribution functions and RMS value is represented to determine a feasible method to reject or reduce vibration related error in position and velocity estimation in inertial navigation. According to a survey conducted by the authors, this is the first time that the effect of the distribution function in vibration related error has been investigated in random vibration testing of INS. Recorded data of navigation grade INS is used in offline static navigation to examine the effect of different characteristics of random vibration tests on navigation error.