• Journal of Applied and Pure Mathematics
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• v.6 no.1_2
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• pp.47-54
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• 2024

In this paper, we investigate the distribution of the zeros of the Bernoulli-Fibonacci polynomials by using computer.

• Communications of the Korean Mathematical Society
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• v.17 no.1
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• pp.1-14
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• 2002

Some recent results on the distribution of zeros of real entire functions are surveyed.

• Journal of the Korean Data and Information Science Society
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• v.15 no.2
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• pp.387-394
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• 2004

Zero-Inflated Poisson distribution is Poisson distribution with excess zeros. Recently defects of product hardley happen in the manufacturing process. In this case it is desirable to apply to the Zero-Inflated Poisson distribution rather than Poisson. Our target of this paper is to study the tests for changes of rate of defects after the unknown change-point. We are going to compare the powers of the two proposed tests with likelihood tests by the simulations.

• Communications for Statistical Applications and Methods
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• v.25 no.2
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• pp.173-184
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• 2018

In medical or public health research, it is common to encounter clustered or longitudinal count data that exhibit excess zeros. For example, health care utilization data often have a multi-modal distribution with excess zeroes as well as a multilevel structure where patients are nested within physicians and hospitals. To analyze this type of data, zero-inflated count models with mixed effects have been developed where a count response variable is assumed to be distributed as a mixture of a Poisson or negative binomial and a distribution with a point mass of zeros that include random effects. However, no study has considered a situation where data are also censored due to the finite nature of the observation period or follow-up. In this paper, we present a weighted version of zero-inflated Poisson model with random effects accounting for variable individual follow-up times. We suggested two different types of weight function. The performance of the proposed model is evaluated and compared to a standard zero-inflated mixed model through simulation studies. This approach is then applied to Medicaid data analysis.

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.425-441
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• 2023

This paper is concerned with the value distribution for meromorphic solutions f of a class of nonlinear partial differential-difference equation of first order with small coefficients. We show that such solutions f are uniquely determined by the poles of f and the zeros of f - c, f - d (counting multiplicities) for two distinct small functions c, d.

• Journal of the Korean Mathematical Society
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• v.44 no.2
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• pp.455-466
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• 2007

The zero-distribution of the Fourier integral $${\int}^{\infty}_{-{\infty}}\;Q(u)e^{p(u)+^{izu}du$$, where P is a polynomial with leading term $-u^{2m}(m\;{\geq}\;1)$ and Q an arbitrary polynomial, is described. To this end, an asymptotic formula for the integral is established by applying the saddle point method.

• Communications of the Korean Mathematical Society
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• v.34 no.2
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• pp.429-437
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• 2019

Dilcher and Stolarsky [1] recently studied a sequence resembling the Chebyshev polynomials of the first kind. In this paper, we follow their some research directions to the Chebyshev polynomials of the second kind. More specifically, we consider a sequence resembling the Chebyshev polynomials of the second kind in two different ways, and investigate its properties including relations between this sequence and the sequence studied in [1], zero distribution and the irreducibility.

• The Pure and Applied Mathematics
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• v.3 no.1
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• pp.47-52
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• 1996

We consider the third order linear homogeneous differential equation L$_3$(y) = y(equation omitted) ＋ P($\chi$)y' ＋ Q($\chi$)y = 0 (E) P($\chi$) $\geq$ 0, Q($\chi$) ＞ 0 and P($\chi$)/Q($\chi$) is nondecreasing on [${\alpha}$, $\infty$) for some real number ${\alpha}$. (1) In this paper we discuss the distribution of zeros of solutions and a condition of oscillatory for equation (E).(omitted)

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2009.10a
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• pp.55-56
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• 2009

• Journal of the Korean Data and Information Science Society
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• v.28 no.3
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• pp.493-504
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• 2017

We often observe count data that exhibit over-dispersion, originating from too many zeros, and under-dispersion, originating from too few zeros. To handle this types of problems, the zero-altered distribution model is designed by Ghosh and Kim in 2007. Their model can control both over-dispersion and under-dispersion with a single parameter, which had been impossible ever. The dispersion type depends on the sign of the parameter ${\delta}$ in zero-altered distribution. In this study, we demonstrate the role of the dispersion type parameter ${\delta}$ through the data of the number of births in Korea. Employing both the chi-square statistic and the Kolmogorov statistic for goodness-of-fit, we also explained any difference between the theoretical distribution and the observed one that exhibits either over-dispersion or under-dispersion. Finally this study shows whether the test statistics for goodness-of-fit show any similarity with the role of the dispersion type parameter ${\delta}$ or not.