• Bulletin of the Korean Mathematical Society
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• v.45 no.2
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• pp.339-353
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• 2008

The distributions of products and ratios of random variables are of interest in many areas of the sciences. In this paper, the exact distributions of the product |XY| and the ratio |X/Y| are derived when X and Y are independent Pearson type VII random variables.

• 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.

• Journal of the Korean Data and Information Science Society
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• v.9 no.2
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• pp.255-262
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• 1998

In this paper, we study the saddlepoint approximations for the ratio of independent random variables. In Section 2, we derive the saddlepoint approximation to the probability density function. In Section 3, we represent a numerical example which shows that the errors are small even for small sample size.

• Journal of the Korean Data and Information Science Society
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• v.21 no.5
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• pp.967-972
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• 2010

We shall consider estimations of an exponetiated parameter of the exponentiated Pareto distribution with known scale and threshold parameters. A quotient distribution of two independent exponentiated Pareto random variables is obtained. We also derive the distribution of the ratio of two independent exponentiated Pareto random variables.

• Journal of the Korean Statistical Society
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• v.23 no.2
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• pp.239-250
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• 1994

In this paper, we prove a strong large deviations theorem for the ratio of independent randoem variables with error rate of $O(n^{-1})$. To obtain our results we use the inversion formula for the tail probability and apply the Chaganty and Sethuraman's (1985) approach.

• Journal of the Korean Data and Information Science Society
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• v.17 no.1
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• pp.187-193
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• 2006

This paper shows how to use continuation-ratio logits for the analysis of structured polytomous data. Here, response categories are considered to have a nested binary structure. Thus, conditionally nested binary random variables can be defined in each step. Two types of factors are considered as independent variables affecting response probabilities. For the purpose of analyzing categorical data with binary nested strutures a continuation-ratio mixed model is suggested. Estimation procedure for the unknown parameters in a suggested model is also discussed in detail by an example.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.221-230
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• 2007

The exponential and the gamma distributions have been the traditional models for drought duration and drought intensity data, respectively. However, it is often assumed that the drought duration and drought intensity are independent, which is not true in practice. In this paper, an application of the bivariate gamma exponential distribution is provided to drought data from Nebraska. The exact distributions of R=X+Y, P=XY and W=X/(X+Y) and the corresponding moment properties are derived when X and Y follow this bivariate distribution.

• Journal of the Korean Data and Information Science Society
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• v.10 no.2
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• pp.415-428
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• 1999

In this paper, we study the saddlepoint approximations for the ratio of two independent sequences of random variables. In Section 2, we review the saddlepoint approximation to the probability density function. In section 3, we derive an saddlepoint approximation formular for the tail probability by following Daniels'(1987) method. In Section 4, we represent a numerical example which shows that the errors are small even for small sample size.

• 한국데이터정보과학회:학술대회논문집
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• 2006.11a
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• pp.37-42
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• 2006

We shall consider an inference of the reliability P(Y

• Journal of the Korean Data and Information Science Society
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• v.7 no.2
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• pp.189-201
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• 1996

In this paper, we study the saddlepoint approximations for the ratio of independent random variables. In Section 2, we derive the saddlepoint approximation to the density. And in Section 3, we derive two approximation formulae for the tail probability, one by following Daniels'(1987) method and the other by following Lugannani and Rice's (1980). In Section 4, we represent some numerical examples which show that the errors are small even for small sample size.