• Communications for Statistical Applications and Methods
• /
• v.23 no.4
• /
• pp.321-334
• /
• 2016

In this paper, we propose power t distribution based on t distribution. We also study the properties of and inferences for power t model in order to solve the problem of real data showing both skewness and heavy tails. The comparison of skew t and power t distributions is based on density plots, skewness and kurtosis. Note that, at the given degree of freedom, the kurtosis's range of the power t model surpasses that of the skew t model at all times. We draw inferences for two parameters of the power t distribution and four parameters of the location-scale extension of power t distribution via maximum likelihood. The Fisher information matrix derived is nonsingular on the whole parametric space; in addition we obtain the profile log-likelihood functions on two parameters. The response plots for different sample sizes provide strong evidence for the estimators' existence and unicity. An application of the power t distribution suggests that the model can be very useful for real data.

• Journal of the Korean Statistical Society
• /
• v.34 no.3
• /
• pp.245-261
• /
• 2005

The marginal distribution of X is considered when (X, Y) has a truncated bivariate t-distribution. This paper mainly focuses on the marginal nontruncated distribution of X where Y is truncated below at its mean and its observations are not available. Several properties and applications of this distribution, including relationship with Azzalini's skew-normal distribution, are obtained. To circumvent inferential problem arises from adopting the frequentist's approach, a Bayesian method utilizing a data augmentation method is suggested. Illustrative examples demonstrate the performance of the method.

• The Korean Journal of Financial Management
• /
• v.25 no.4
• /
• pp.79-116
• /
• 2008

This paper examines and estimates GARCH-VaR models (RiskMetrics, GARCH, IGARCH, GJR and APARCH) with three different distributions such as Gaussian normal, Student-t, Skewness Student-t Distribution using the daily price data from Korean Stock Market during Jan. 1, 1980-Sept. 30, 2004. It also compares them. In-sample test, this finds that for all confidence level as $90%{\sim}99.9%$, the performance and accuracy of IGARCH with ${\lambda}=0.87$ and skewness Student-t distribution are superior to other models and distributions in long position, but GARCH and GJR with Skewness Student-t distribution in short position. For above 99% confidence level, the performance and accuracy of IGARCH with ${\lambda}=0.87$ in both long and short positions are superior to other models and distributions, but Skewness Student-t distribution for long position and Student-t distribution for short position are more accuracy and superior to other distributions. In-out-of sample test, these results also confirm the evidences that the above findings are consistent as well.

• Journal of the Korean Statistical Society
• /
• v.34 no.2
• /
• pp.109-123
• /
• 2005

Variogram estimation is an important step of spatial statistics since it determines the kriging weights. Matheron's variogram estimator can be written as a quadratic form of the observed data. In this paper, we extend a skew t distribution to a generalized skew t distribution and moments of the variogram estimator for a generalized skew t distribution are derived in closed forms. After calculating the correlation structure of the variogram estimator, variogram fitting by generalized least squares is discussed.

• Journal of the Korean Statistical Society
• /
• v.34 no.4
• /
• pp.311-329
• /
• 2005

Skewed t distributions have attracted significant attention in the last few years. In this paper, a generalization - referred to as the skewed generalized t distribution - with the pdf f(x) = 2g(x)G(${\lambda}x$) is introduced, where g(${\cdot}$) and G (${\cdot}$) are taken, respectively, to be the pdf and the cdf of the generalized t distribution due to McDonald and Newey (1984, 1988). Several particular cases of this distribution are identified and various representations for its moments derived. An application is provided to rainfall data from Orlando, Florida.

• Journal of Environmental Impact Assessment
• /
• v.23 no.4
• /
• pp.285-295
• /
• 2014

In this study, we analyzed probability distribution of EMCs (Event Mean Concentration) of COD, TOC, T-N, T-P and SS from rice paddy fields and compared the mean values of observed EMCs and the median values of estimated EMCs ($EMC_{50}$) through probability distribution. The field monitoring was conducted during a period of four crop-years (from May 1, 2008, to September 30. 2011) in a rice cultivation area located in Emda-myun, Hampyeong gun, Jeollanam-do, Korea. Four probability distributions such as Normal, Log-normal, Gamma, and Weibull distribution were used to fit values of EMCs from rice paddy fields. Our results showed that the applicable probability distributions were Normal, Log-normal, and Gamma distribution for COD, and Normal, Log- Normal, Gamma and Weibull distribution for T-N, and Log-normal, Gamma and Weibull distribution for T-P and TOC, and Log-normal and Gamma distribution for SS. Log-normal and Gamma distributions were acceptable for EMCs of all water quality constituents(COD, TOC, T-N, T-P and SS). Meanwhile, mean value of observed COD was similar to median value estimated by the gamma distribution, and TOC, T-N, T-P, and SS were similar to median value estimated by log-normal distribution, respectively.

• Management & Information Systems Review
• /
• v.34 no.3
• /
• pp.141-160
• /
• 2015

IoT(Internet of Things) has become a major issue as new type of convergence technology, expending existing of USNs(Ubiquitous Sensor Networks), NFC(Near Field Communication), and M2M(Machine to Machine). The IoT technology defines as a networking for things, which can establish intelligent links collaboratively for sensing networking and processing between each other without human intervention. The purpose of this study is to investigate to forecast the future distribution changes and orientation of contribution of distribution industry on IoT and to provide the implication of distribution changes. To become a global market leader, IoT requires much more development of core technology of IoT for distribution industry, new service creation and try to use a market-based demand side strategy to create markets. So, to become a global leader in distribution industry, this study results show that first of all establishment of standardization of IoT, privacy safeguards, security issues, stability and value were more important than others. The research findings suggest that the development goals of IoT should strive to boost the creation of a global leader in distribution industry and convenience to consider consumers' demands as the most important thing.

• Journal for History of Mathematics
• /
• v.13 no.1
• /
• pp.1-14
• /
• 2000

The first part of this thesis discusses the Pearson's Curve Family which gives $\beta$distribution, $\Gamma$-distribution, $X^2$-distribution and t-distribution. The second part of this thesis gives some brief process of calculations for normal distribution density and t-distribution density by the 7-th type Curve of Pearson's Curve Family. Finally, a conclusion arrives that Student(Gosset) could not find out his famous 'Student's t-distribution' without his attending of 'Pearson's Differential Equation' class taught by Pearson himself when he was a senior student. However, if he had got a professorship at the Pearson Statistics Laboratory, the University of London, then he could not have found 'Student's t-distribution' for small sampling technique of modern statistics.

• East Asian mathematical journal
• /
• v.35 no.1
• /
• pp.67-75
• /
• 2019

We investigate the averaging value of a random sampling of a Dirichlet series with some condition using Poisson distribution. Our result is the following: Let $L(s)={\sum}^{\infty}_{n=1}{\frac{a_n}{n^s}}$ be a Dirichlet series that converges absolutely for Re(s) > 1. If $X_t$ is an increasing random sampling with Poisson distribution and there exists a number $0<{\alpha}<{\frac{1}{2}}$ such that ${\sum}_{n{\leq}u}a_n{\ll}u^{\alpha}$, then we have $${\mathbb{E}}L(1/2+iX_t)=O(t^{\alpha}{\sqrt{{\log}t}})$$, for all sufficiently large t in ${\mathbb{R}}$. As a result, we get the behaviour of $L({\frac{1}{2}}+it)$ such that L is a Dirichlet L-function or a modular L-function, when t is sampled by the Poisson distribution.

• Journal of the Korean Data and Information Science Society
• /
• v.7 no.2
• /
• pp.273-281
• /
• 1996

It is derived that conditions of counting process ($\{N(t){\mid}t\;{\geq}\;0\}$) in which the number of events in time interval [0, t] has a (n, n+1)-generalized Poisson distribution with parameters (${\theta}t,\;{\lambda}$) and a generalized inflated Poisson distribution with parameters (${\{\lambda}t,\;{\omega}\}$.