• The Korean Journal of Applied Statistics
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• v.30 no.4
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• pp.513-528
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• 2017

Statistics are often used to test two samples if they have been drawn from the same underlying distribution. In this paper, we introduce several well-known distribution-free tests to compare distributions and conduct an extensive Monte-Carlo simulation to specify their behaviors. We consider various circumstances of when two distributions vary in (1) location, (2) scale, (3) symmetry, (4) kurtosis, (5) tail weight. A practical guideline for two-sample goodness-of-fit test is presented based on the simulation result.

• The Korean Journal of Applied Statistics
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• v.17 no.3
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• pp.507-518
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• 2004

Malkovich & Afifi (1973) generalized the univariate skewness and kurtosis to test a hypothesis of multivariate normality by use of the union-intersection principle. However these statistics are hard to compute for high dimensions. We propose the approximate statistics to them, which are practical for a high dimensional data set. We also compare the proposed statistics to Mardia(1970)'s multivariate skewness and kurtosis by a Monte Carlo study.

• The Korean Journal of Applied Statistics
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• v.29 no.4
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• pp.741-752
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• 2016

Numerous studies have shown that normal inverse Gaussian (NIG) distribution adequately fits the empirical return distribution of financial securities. The estimation of parameters can also be done relatively easily, which makes the NIG distribution more useful in financial markets. The maximum likelihood estimation and the method of moments estimation are easy to implement; however, we may encounter a problem in practice when a relationship among the moments is violated. In this paper, we investigate this problem in the parameter estimation and try to find a simple solution through simulations. We examine the effect of our adjusted estimation method with real data: daily log returns of KOSPI, S&P500, FTSE and HANG SENG. We also checked the performance of our method by computing the value at risk of daily log return data. The results show that our method improves the stability of parameter estimation, while it retains a comparable performance in goodness-of-fit.

• Convergence Security Journal
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• v.7 no.2
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• pp.1-8
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• 2007

Finite failure NHPP models presented in the literature exhibit either constant, monotonic increasing or monotonic decreasing failure occurrence rates per fault (intensity function). In this paper, intensity function of Goel-Okumoto model was reviewed, proposes Kappa (2) and the Burr distribution, which maked out efficiency application for software reliability. Algorithm to estimate the parameters used to maximum likelihood estimator and bisection method. For model determination and selection, explored goodness of fit (the error sum of squares) The methodology developed in this paper is exemplified with a software reliability real data set introduced by NTDS (Naval Tactical Data System)

• Knowledge Management Research
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• v.22 no.2
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• pp.247-268
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• 2021

Investors mainly use PER and PBR among financial ratios for valuation and investment decision-making. I conduct an analysis of two basic financial ratios from a statistical perspective. Financial ratios contain key accounting numbers which reflect firm fundamentals and are useful for valuation or risk analysis such as enterprise credit evaluation and default prediction. The distribution of financial data tends to be extremely heavy-tailed, and PER and PBR show exceedingly high level of kurtosis and their extreme cases often contain significant information on financial risk. In this respect, Extreme Value Theory is required to fit its right tail more precisely. I introduce not only GPD but exGPD. GPD is conventionally preferred model in Extreme Value Theory and exGPD is log-transformed distribution of GPD. exGPD has recently proposed as an alternative of GPD(Lee and Kim, 2019). First, I conduct a simulation for comparing performances of the two distributions using the goodness of fit measures and the estimation of 90-99% percentiles. I also conduct an empirical analysis of Information Technology firms in Korea. Finally, exGPD shows better performance especially for PBR, suggesting that exGPD could be an alternative for GPD for the analysis of financial ratios.