• Journal of the Korean Statistical Society
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• v.21 no.2
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• pp.187-200
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• 1992

Samples are often found to be too heterogeneous to be explained by a one-parameter family of models in the sense that the implicit mean-variance relationship in such a family is violated by the data. This phenomenon is often called over-dispersion. The most frequently used method in dealing with over-dispersion is to mix a one-parameter family creating a two parameter marginal mixture family for the data. In this paper, we investigate performance of estimators such as maximum likelihood estimator, method of moment estimator, and maximum quasi-likelihood estimator in negative binomial and beta-binomial distribution. Simulations are done for various mean parameter and dispersion parameter in both distributions, and we conclude that the moment estimators are very superior in the sense of bias and asymptotic relative efficiency.

• 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.

• Journal of applied mathematics & informatics
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• v.35 no.3_4
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• pp.241-260
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• 2017

An analysis is made to study the solute transport in a Casson fluid flow through an annulus in presence of oscillatory flow field and determine how this flow influence the solute dispersion along the annular region. Axial dispersion coefficient and the mean concentration expressions are calculated using the generalized dispersion model. Dispersion coefficient in oscillatory flow is found to be a function of frequency parameter, Schmidt number, and the pressure fluctuation component besides its dependency on yield stress of the fluid, annular gap and time in the case of steady flow. Due to the oscillatory nature of the flow, the dispersion coefficient changes cyclically and the amplitude and magnitude of the dispersion increases initially with time and reaches a non - transient state after a certain critical time. This critical value varies with frequency parameter and independent of the other parameters. It is found that the presence of inner cylinder and increase in the size of the inner cylinder inhibits the dispersion process. This model may be used in understanding the dispersion phenomenon in cardiovascular flows and in particular in catheterized arteries.

• The Journal of the Acoustical Society of Korea
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• v.18 no.4
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• pp.47-52
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• 1999

In this paper, we proposed a new approach to weight each feature parameter by considering the dispersion of feature parameters and its degree of contribution to recognition rate. We determined the total distribution factor that is proportional to recognition rate of each feature parameter and the dispersion factor according to the dispersion of each feature parameter. Then. we determined state-dependent weighting using the total distribution factor and dispersion factor. To verify the validity of the proposed approach, recognition experiments were performed using the PLU(Phoneme-Like Unit)-based HMM. Experimental results showed the improvement of 7.7% at the recognition rate using the proposed method.

• Journal of Power System Engineering
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• v.21 no.5
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• pp.79-85
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• 2017

Vickers hardness is an important material in the design and reliability is required. Therefore, these values are very important as the basic data for design, manufacture and development, and the identification of quantitative probability distribution characteristics such as mean and dispersion is a very important parameter in design. In this study, Vickers hardness was measured after artificially heat-treated in the temperature range 753K, where chrome depletion near the grain boundary occurred for three kinds of stainless steels, and the Vickers hardness were evaluated. From the results, Vickers hardness increased with increasing heat treatment temperature. In Weibull distribution for Vickers hardness, the dispersion of STS310S at 813K and 873K was small, and the dispersion of STS316L at 753K, 933K and 993K was small. Also, STS347H exhibited the lowest dispersion at 753K in three kinds of stainless steels. The scale parameter increased with increasing heat treatment temperature in three kinds of stainless steels.

• The Korean Journal of Applied Statistics
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• v.30 no.1
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• pp.95-102
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• 2017

Gamma generalized linear models have received less attention than Poisson and binomial generalized linear models. Therefore, many old-established statistical techniques are still used in gamma generalized linear models. In particular, existing literature and textbooks still use approximate estimates for the dispersion parameter. In this paper we study the efficiency of various dispersion parameter estimators in gamma generalized linear models and perform numerical simulations. Numerical studies show that the maximum likelihood estimator and Cox-Reid adjusted maximum likelihood estimator are recommended and that approximate estimates should be avoided in practice.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.979-991
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• 2022

A special class of exponential dispersion models is the class of Tweedie distributions. This class is very significant in statistical modeling as it includes a number of familiar distributions such as Gaussian, Gamma and compound Poisson. A Tweedie distribution has a power parameter p, a mean m and a dispersion parameter 𝜙. The value of the power parameter lies in identifying the corresponding distribution of the Tweedie family. The basic objective of this research work resides in investigating the existence of the implicit estimator of the power parameter of the Tweedie distribution. A necessary and sufficient condition on the mean parameter m, suggesting that the implicit estimator of the power parameter p exists, was established and we provided some asymptotic properties of this estimator.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.23 no.2
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• pp.218-225
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• 1999

Flow visualization study has been conducted to simulate the turbulent dispersion behavior of a crossflow jet physically under the conditions of various thermal stratification in a wind tunnel. A smoke jet with the constant ratio of the jet to freestream velocity is injected normally to the cross flow of the thermally stratified wind tunnel(TSWT) for flow visualization. The typical natures of the smoke dispersion under different thermal stratifications such as neutral, weakly stable, strongly stable, weakly unstable, strongly unstable and inversion layer are successfully reproduced in the TSWT. The Instantaneous velocity and temperature fluctuations are measured by using a cold and hot-wire combination probe. The time averaged dispersion behaviors, the centerline trajectories, the spreading angles and the virtual origins of the cross jet are deduced from the edge detected images with respect to the stability parameter. All the general characteristics of the turbulent dispersion behavior reveal that the definitely different dispersion mechanisms are inherent in both stable and unstable conditions. It is conjectured that the turbulent statistics obtained in the various stability conditions quantitatively demonstrate the vertical scalar flux plays a key role in the turbulent dispersion behavior.

• Bulletin of the Korean Mathematical Society
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• v.48 no.4
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• pp.839-845
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• 2011

In this paper, we consider the cusum of squares test for the dispersion parameter in stochastic differential equation models. It is shown that the test has a limiting distribution of the sup of a Brownian bridge, unaffected by the drift parameter estimation. A simulation result is provided for illustration.

• Journal of the Korean Data and Information Science Society
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• v.28 no.1
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• pp.153-161
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• 2017

Branching processes which is used for epidemic dispersion as stochastic process model have advantages to estimate parameters by real data. We have to estimate both mean and dispersion parameter in order to use the negative binomial distribution as an offspring distribution on branching processes. In existing studies on biology and epidemiology, it is estimated using maximum-likelihood methods. However, for most of epidemic data, it is hard to get the best precision of maximum-likelihood estimator. We suggest a Bayesian inference that have good properties of statistics for small-sample. After estimating dispersion parameter we modelled the posterior distribution for 2015 Korea MERS cases. As the result, we found that the estimated dispersion parameter is relatively stable no matter how we assume prior distribution. We also computed extinction probabilities on branching processes using estimated dispersion parameters.