• Journal of the Korean Statistical Society
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• v.1 no.1
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• pp.11-17
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• 1973

A class of sequential binomial tests and a sequential rank test can be applied for testing two treatments when subjects are paired in many-to-one ratio. The efficiency of each test is examined in terms of the average sample number. The binomial tests are much easier and more convenient to apply than the rank test not as efficient. Within the class of binomial test, the median test appears to be the most efficient is general.

• Journal of the Korean Statistical Society
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• v.11 no.2
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• pp.131-138
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• 1982

Analogous to Singh's (1978) characterization of positive-Poisson distributioin and Shanmugam and Singh's (1992) characterization of logarithmic series distribution, a characterization and its statistical application of the negative binomial distribution truncated at zero are given in this paper. While it is known that under certain conditions the negative binomial distribution truncted at zero approaches the positive-Poisson and the logarithmic series distributions, we show here that the results of this paper approach in limit the results of Singh, and Shanmugam and Singh, respectively. Using the biologicla data from Sampford (1955), we illusrate our results. Also, expressions are explicitly given to test the hypothesis whether a random sample is indeed from a geometric distribution.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.61-68
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• 2022

Let M_p := 2^p - 1 be a Mersenne prime. In this article, we find integers a, b, c, d, e and n satisfying $\sum_{t=0}^{n}\;\({an+b\\ct+d}\)\;=\;M_{p^e}$ given a Mersenne prime number M_p. In order to find a special case that satisfies the above results, we reprove an well-known relation of a certain sum of binomial coefficients and a divisor function.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.517-530
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• 2015

In this paper, we establish a class of strong limit theorems, represented by inequalities, for the arbitrary random field with respect to the product binomial distributions indexed by the infinite tree on the generalized random selection system by constructing the consistent distri-bution and a nonnegative martingale with pure analytical methods. As corollaries, some limit properties for the Markov chain field with respect to the binomial distributions indexed by the infinite tree on the generalized random selection system are studied.

• Communications for Statistical Applications and Methods
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• v.23 no.5
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• pp.433-444
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• 2016

When we observe binary responses in a cluster (such as rat lab-subjects), they are usually correlated to each other. In clustered binomial counts, the independence assumption is violated and we encounter an extra-variation. In the presence of extra-variation, the ordinary statistical analyses of binomial data are inappropriate to apply. In testing the homogeneity of proportions between several treatment groups, the classical Pearson chi-squared test has a severe flaw in the control of Type I error rates. We focus on modifying the chi-squared statistic by incorporating variance inflation factors. We suggest a method to adjust data in terms of dispersion estimate based on a quasi-likelihood model. We explain the testing procedure via an illustrative example as well as compare the performance of a modified chi-squared test with competitive statistics through a Monte Carlo study.

• Industrial Engineering and Management Systems
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• v.10 no.2
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• pp.170-177
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• 2011

We present an improved binomial method for pricing financial deriva-tives by using cell averages. After non-overlapping cells are introduced around each node in the binomial tree, the proposed method calculates cell averages of payoffs at expiry and then performs the backward valuation process. The price of the derivative and its hedging parameters such as Greeks on the valuation date are then computed using the compact scheme and Richardson extrapolation. The simulation results for European and American barrier options show that the pro-posed method gives much more accurate price and Greeks than other recent lattice methods with less computational effort.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.225-242
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• 2017

A family of $Ap{\acute{e}}ry$-like series involving reciprocals of central binomial coefficients is studied and it is shown that they represent transcendental numbers. The structure of such series is further examined in terms of finite combinations of logarithms and arctangents with arguments and coefficients belonging to a suitable algebraic extension of rationals. Monotonicity of certain quotients of weighted binomial sums which arise in the study of competitive cheap talk models is established with the help of a continuous extension of the discrete model at hand. The monotonic behavior of such quotients turns out to have important applications in game theory.

• Journal of the Korean Data and Information Science Society
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• v.21 no.4
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• pp.737-745
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• 2010

In this paper, various methods for finding confidence intervals for the p of binomial parameter are reviewed. We compare the performance of several confidence interval estimates in terms of actual coverage probability by small sample Monte Carlo simulation.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.2
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• pp.15-29
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• 2007

In this paper, we explore some interesting models of the quasi-negative-binomial distribution based on difference differential equations applicable to theory of microorganisms and the situations like that. Some characterizations based on conditional distributions and damage process have been obtained. Further, the distribution of number of accidents as the quasi-negative-binomial distribution in the light of Irwin's theory of ";proneness-liability"; model has been derived. Finally, the proposed model (QNBD) has been applied to study the Shunting accidents, home injuries, and strikes in industries.

• Magazine of the Korean Society of Agricultural Engineers
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• v.30 no.4
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• pp.109-116
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• 1988

This study was aimed at determining a regime of flow through rubble mound dike consisted of all sized quarrystons, and deriving a relationship between hydraulic gradient (I) and mean flow velocity (V) through the dike. The analysis was carried out with the data observed after final gap closing of the Haenam Sea dike from May, 6 to May, 14, 1987. The resu]ts are summarized as follows: 1. The regime of flow would be defined as the turbulent flow. 2. As to the relationships, two kinds of formula that are exponential and binomial were obtained. Exponential formula: I=2.099V 1.2888 Binomial formula: I=0.6113V+5.5235V$^2$ 3. Correlation coefficient of the former was 0.824 and that of the latter was 0.821, and the deviations between observed data and estimated were 0.0070 and 0.0064 respectively. 4. Comparing the correlation coefficient, both the equations have the same correlation coefficients, but in case of the deviation the binomial equation was better than the exponential equation. Therefore, the binomial equation is proposed for analyzing the flow through rubble mound dike.