• Publications of The Korean Astronomical Society
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• v.30 no.2
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• pp.261-263
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• 2015

The metallicity distribution of globular clusters (GCs) provides a crucial clue for the star formation history of their host galaxy. With the assumption that GCs are generally old, GC colors have been used as a proxy for GC metallicities. Bimodal color distributions of GCs observed in most large galaxies have, for decades, been interpreted as bimodal metallicity distributions, indicating the presence of two populations within a galaxy. However, the conventional view has been challenged by a new theory that non-linear GC color-metallicity relations can cause a bimodal color distribution even from a single-peaked metallicity distribution. Using photometric and spectroscopic data of NGC 5128 GCs in combination with stellar population simulation models, we examine the effect of non-linearity in GC color-metallicity relations on transformation of the color distributions into the metallicity distributions. Although in some colors offsets are present between observations and models for the color-metallicity relations, their overall shape agrees well for various colors. After the offsets are corrected, the observed spectroscopic metallicity distribution is well reproduced via modeled color-metallicity relations from various color distributions having different morphologies. We discuss the implications of our results.

• Journal of the Korean Data and Information Science Society
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• v.25 no.6
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• pp.1231-1239
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• 2014

In this paper we analyse the distributions of the number of goals scored by home teams and away teams in K-league soccer outcomes between 1983 and 2012. Real soccer data is explained in K-league using statistical distributions such that Poisson, negative binomial, extreme value and zero inflated Poisson. How close the goals of home and away fits the different distributions are tested by performing chi-square goodness of fit tests. According to these tests, the Poisson distribution gives the best fit to the home goals data. But it is best to model the away goals data on zero inflated Poisson distribution. Also, there is some weak evidence of the dependence for home and away goals.

• Communications for Statistical Applications and Methods
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• v.28 no.5
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• pp.411-424
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• 2021

Inference following two-stage adaptive designs (also known as two-stage randomization designs) with survival endpoints usually focuses on estimating and comparing survival distributions for the different treatment strategies. The aim is to identify the treatment strategy(ies) that leads to better survival of the patients. The objectives of this study were to assess the performance three commonly cited methods for estimating survival distributions in two-stage randomization designs. We review three non-parametric methods for estimating survival distributions in two-stage adaptive designs and compare their performance using simulation studies. The simulation studies show that the method based on the marginal mean model is badly affected by high censoring rates and response rate. The other two methods which are natural extensions of the Nelson-Aalen estimator and the Kaplan-Meier estimator have similar performance. These two methods yield survival estimates which have less bias and more precise than the marginal mean model even in cases of small sample sizes. The weighted versions of the Nelson-Aalen and the Kaplan-Meier estimators are less affected by high censoring rates and low response rates. The bias of the method based on the marginal mean model increases rapidly with increase in censoring rate compared to the other two methods. We apply the three methods to a leukemia clinical trial dataset and also compare the results.

• Communications for Statistical Applications and Methods
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• v.28 no.1
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• pp.1-19
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• 2021

Heavy tailed distributions are useful for modeling actuarial and financial risk management problems. Actuaries often search for finding distributions that provide the best fit to heavy tailed data sets. In the present work, we introduce a new class of heavy tailed distributions of a special sub-model of the proposed family, called a new extended alpha power transformed Weibull distribution, useful for modeling heavy tailed data sets. Mathematical properties along with certain characterizations of the proposed distribution are presented. Maximum likelihood estimates of the model parameters are obtained. A simulation study is provided to evaluate the performance of the maximum likelihood estimators. Actuarial measures such as Value at Risk and Tail Value at Risk are also calculated. Further, a simulation study based on the actuarial measures is done. Finally, an application of the proposed model to a heavy tailed data set is presented. The proposed distribution is compared with some well-known (i) two-parameter models, (ii) three-parameter models and (iii) four-parameter models.

• Journal of Forest and Environmental Science
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• v.39 no.2
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• pp.96-104
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• 2023

The successful restoration program requires a comprehensive understanding of variables influencing seedling efficiency. Below-ground is hypothesized to have a major impact on seedling performance of species when planted in agriculture, and degraded areas with different types of mulching. This study investigated on Sg. Terla Forest Reserve in Cameron Highlands Pahang, Malaysia. In this study randomized complete block design (RCBD) was used. The excavation method was applied to study the root system development, above, and below ground biomass distributions under different types of mulching: coconut mulching (CM), oil palm mulching (OM), plastic mulching (PM) and control (CK). The root diameter, main root length, lateral root length, root coiling, and root direction toward to sun were recorded. The results in this study indicate that mulching had significant effect on root diameter, main root length, and root distributions among treatments while for lateral root length, root: shoot ratio, dry biomass distributions, and above and below ground biomass did not showed significant effect among treatments. The highest values for root diameter, lateral root length, main root length, root distributions, dry biomass distributions and above and below ground biomass were showed in CM treatments. However 75% of root coiling was observed in seedlings between treatments.

• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.467-482
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• 2000

Testing equality of two and k distributions has long been an interesting issue in statistical inference. To overcome the sparseness of data points in high-dimensional space and deal with the general cases, we suggest several projection pursuit type statistics. Some results on the limiting distributions of the statistics are obtained, some properties of Bootstrap approximation are investigated. Furthermore, for computational reasons an approximation for the statistics the based on Number theoretic method is applied. Several simulation experiments are performed.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.111-118
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• 2013

External excitations are employed to investigate properties of optical media, with measurement data often analyzed via linear response theory. In this respect, external forcing is modeled here by well-known Poisson and negative-binomial distributions. Ensuing dynamics is examined with a special attention to the relative decay rates of damped harmonic oscillators to such external forcing, along with its relationship to other physical phenomena.

• Journal of the Korean Data and Information Science Society
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• v.25 no.1
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• pp.255-261
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• 2014

Many studies have estimated a mixture of binomial distributions. This paper considers an extension, a mixture of shifted binomial distributions, and the estimation of the distribution. The range of each component binomial distribution is rst evaluated and then for each possible value of shifted parameters, the EM algorithm is employed to estimate those parameters. From a set of possible value of shifted parameters and corresponding estimated parameters of the distribution, the likelihood of given data is determined. The simulation results verify the performance of the proposed method.

• Journal of the Korean Mathematical Society
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• v.35 no.3
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• pp.675-690
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• 1998

A role of singletons in quantum central limit theorems is studied. A common feature of quantum central limit distributions, the singleton condition which guarantees the symmetry of the limit distributions, is revisited in the category of discrete groups and monoids. Introducing a general notion of quantum independence, the singleton independence which include the singleton condition as an extremal case, we clarify the role of singletons and investigate the mechanism of arising non-symmetric limit distributions.

• Communications for Statistical Applications and Methods
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• v.14 no.1
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• pp.93-109
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• 2007

In this paper we study a number of new exponentiated distributions. The survival function, failure rate and moments of the distributions have been derived using certain special functions. The behavior of the failure rate has also been studied.