• Journal of the Korean Data and Information Science Society
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• 제20권1호
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• pp.219-223
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• 2009

We shall derive a quotient distribution of two independent gamma variables and its moment and reliability are represented by hypergeometric function and Wittaker's function. And we shall consider an inference on the reliability in two independent gamma random variables.

• Journal of the Korean Statistical Society
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• 제13권1호
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• pp.42-47
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• 1984

In this paper, the means of the estimators for the coefficient of variation (CV) in an underlying Pareto distribution are expressed in terms of confluent hypergeometric functions. The numericla values of the biases for the CV estimators in the Pareto distribution are also obtained.

• 한국수학교육학회지시리즈A:수학교육
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• 제29권2호
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• pp.79-93
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• 1990

In this thesis the following studies have been tried: 1. To estimate reliability and validity of the items of scholastic achievment tests that had been tested by the evaluation service centers. 2. To smooth the sample frequency distribution of observed scores and to estimate the frequency distribution of observed scores approximating to the Negative Hypergeometric Distribution.

• Journal of the Korean Data and Information Science Society
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• 제16권3호
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• pp.581-589
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• 2005

The purpose of this thesis is to develop and introduce Add-in program which we can systematically, visually and dynamically study discrete probability distribution of binomial distribution, poisson distribution and hypergeometric distribution, and continuous probability distribution of normal distribution, exponential distribution, and the definition and characteristics of t distribution, F distribution and ${\chi}^2$ distribution to be driven from normal distribution, and graphs, the computation process of probability by using VBA which is the device of Excel.

• Journal of the Korean Statistical Society
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• 제17권1호
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• pp.46-55
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• 1988

Two-piece double exponential distribution (TPDE) with one piece $(X \leq 0)$ having the scale parameter $\theta_1$ while the other piece (X>0) having $\theta_2$ is considered here. Distribution of the sum of n-independent variables from such a distribution is obtained. Special cases of this distribution are also treated. Next, distribution of the ratio of two independent (TPDE) variables is derived. As an extension, distribution of $x_1/x_2x_3$ is expressed terms of hypergeometric functions. A small table gives the power of the test regarding double exponential against (TPDE).

• Journal of the Korean Data and Information Science Society
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• 제1권
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• pp.67-76
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• 1990

For a two-parameter Pareto distribution, the uniformly minimum variance unbiased estimateors(UMVUE) for the function of the two parameters are expressed in terms of confluent hypergeometric function. The variance of the UMVUE is also expressed in terms of hypergeometric function of several variables. UMVUE's for the ${\gamma}th$ moment about zero and several useful parametric functions, and their variances are obtained as special cases. The estimators of Baxter(1980) and Saksena and Johnson(1984) are special cases of our estimator.

• Journal of the Korean Data and Information Science Society
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• 제21권5호
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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 Data and Information Science Society
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• 제23권1호
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• pp.219-225
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• 2012

We derive approximate maximum likelihood estimators of two parameters in a weighted exponential distribution, and derive the density function for the ratio Y=(X+Y) of two independent weighted exponential random variables X and Y, and then observe the skewness of the ratio density.

• Communications for Statistical Applications and Methods
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• 제5권1호
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• pp.265-275
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• 1998

In testing the partial association between two variables after controlling for the S levels of a third factor, the Mantel and Haenszel (1959) statistic is often used. Since the statistic is based on the asymptotic distribution of the sum X of S hypergeometric variates, a guideline for the minimum requirements for the application of the statistic is useful. Mantel and Fleiss (1980) developed a criterion based on the guideline for the Pearson's $X^2$ statistic. The criterion requires the distance from the expected value to the closer bound of X to be at least five. The Mantel-Fleiss (MF) criterion was studied through a simulation using the hypergeometric sampling scheme. The criterion is not satisfactory. The size of statistic exceeded nominal 0.05 level nearly 1/5 of the cases even when the criteion is met. However, the results show that the statistic is much more unstable and conservative when the criterion is not met.

• Journal of the Korean Data and Information Science Society
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• 제23권6호
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• pp.1213-1222
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• 2012

We shall derive the moment of the ratio Y/(X + Y) and the reliability P(X < Y ), and then observe the skewness of the ratio in a bivariate Pareto density function of (X, Y). And we shall consider an approximate MLE of parameters in the bivariate Pareto density function.