• 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 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.36 no.4
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• pp.479-488
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• 2007

The elliptic random field is an extension to the Gaussian random field. We proved a theorem which characterizes the elliptic random field. We proposed a heuristic approach to derive an approximation to the distribution of the size of one connected component of its excursion set above a high threshold. We used this approximation to approximate the distribution of the largest cluster size. We used simulation to compare the approximation with the exact distribution.

• Bulletin of the Korean Mathematical Society
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• v.45 no.3
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• pp.509-522
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• 2008

The main aim of this paper is to present some results related to asymptotic behavior of distribution functions of random variables of chi-square type $X^2_N={\Sigma}^N_{i=1}\;X^2_i$ with degrees of freedom N, where N is a positive integer-valued random variable independent on all standard normally distributed random variables $X_i$. Two ways for computing the distribution functions of chi-square type random variables with random degrees of freedom are considered. Moreover, some tables concerning considered distribution functions are demonstrated in Appendix.

• 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.

• Journal of the Korean Mathematical Society
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• v.42 no.1
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• pp.171-189
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• 2005

In this paper, we first establish some characterization of tightness for a sequence of random elements taking values in the space of normal and upper-semicontinuous fuzzy sets with compact support in $R^P$. As a result, we give some sufficient conditions for a sequence of fuzzy random sets to converge in distribution.

• Journal of the Korean Data and Information Science Society
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• v.7 no.1
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• pp.105-112
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• 1996

Softwares including random number generation are abundant in modern informative society. But it's hard to get directly multivariate multinomial random numbers from existing softwares. Multivariate multinomial random numbers are greatly used in social and medical sciences. In this paper, we show that desired multivariate multinomial random numbers can be easily generated by the aids of existing random number generating software. Some characteristics of multivariate multinomial distribution are surveyd. Measures of association for the generated random numbers were computed and compared with population ones via simulation study.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.2
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• pp.421-426
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• 2013

We give a series of discrete random variables which converges to a random variable whose distribution function is the Riesz-N$\acute{a}$gy-Tak$\acute{a}$cs (RNT) distribution. We show this using the correspondence theorem that if the moments coincide then their corresponding distribution functions also coincide.

• 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.

• Computers and Concrete
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• v.33 no.2
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• pp.147-162
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• 2024

This study presents a random-aggregate mesoscale model integrating the random distribution of the coarse aggerates and the damage mechanics of the mortar and interfacial transition zone (ITZ). This mesoscale model can generate the random distribution of the coarse aggregates according to the prescribed particle size distribution which enables the automation of the current methodology with different coarse aggregates' distribution. The main innovation of this work is to propose the "correction factor" to eliminate the dimensionally dependent mesh sensitivity of the concrete damaged plasticity (CDP) model. After implementing the correction factor through the user-defined subroutine in the randomly meshed mesoscale model, the predicted fracture resistance is in good agreement with the average experimental results of a series of geometrically similar single-edge-notched beams (SENB) concrete specimens. The simulated cracking pattern is also more realistic than the conventional concrete material models. The proposed random-aggregate mesoscale model hence demonstrates its validity in the application of concrete fracture failure and statistical size effect analysis.