The Use of Generalized Gamma-Polynomial Approximation for Hazard Functions

하형태 한국통계학회 2009 응용통계연구 Vol.22 No.6

We introduce a simple methodology, so-called generalized gamma-polynomial approximation, based on moment-matching technique to approximate survival and hazard functions in the context of parametric survival analysis. We use the generalized gamma-polynomial approximation to approximate the density and distribution functions of convolutions and finite mixtures of random variables, from which the approximated survival and hazard functions are obtained. This technique provides very accurate approximation to the target functions, in addition to their being computationally efficient and easy to implement. In addition, the generalized gamma-polynomial approximations are very stable in middle range of the target distributions, whereas saddlepoint approximations are often unstable in a neighborhood of the mean.

On the Krawtchouk expansion for estimating counting data

하형태 한국데이터정보과학회 2019 한국데이터정보과학회지 Vol.30 No.3

We propose Krawtchouk expansion estimates for modeling count data. The proposed estimate is based on series expansions of discrete Krawtchouk orthogonal polynomials around a binomial distribution. The parameters of the proposed expansion can be estimated via the method of moments or the maximum likelihood method. The proposed expansion is flexible to model under-, equi- and over dispersed data. The classical Weldon's data was revisited to show the flexibility and accuracy of the proposed expansion.

Transformed Jacobi polynomial density and distribution approximations

하형태 한국데이터정보과학회 2018 한국데이터정보과학회지 Vol.29 No.4

A density approximation method by making use of transformed Jacobi orthogonal polynomials is developed for approximating the density and distribution functions of random variables with various compact supports. The method is formulated by a product of a generalized Beta density function and a linear combination of the cor-responding Jacobi orthogonal polynomials, where the infinite sequence of the Jacobi orthogonal polynomials can be generated from the initial approximation of the generalized Beta density function. The moment matching technique was used to estimate parameters of the initial approximation and the coefficients of the linear combination in terms of the exact moments of the target distribution. The numerical examples using an artificial mixture of non-standard density functions and a test statistic show that the proposed method provides excellent density and distribution approximants.

Resampling modifications for the Bagai test

김영민,하형태 한국데이터정보과학회 2018 한국데이터정보과학회지 Vol.29 No.2

In this paper, we develop resampling modifications for the Bagai statistics to test two competing risks model, and make their numerical comparisons in terms of coverage probabilities and statistical powers.We found that the bias-corrected bootstrap method consistently improves on the Jackknife, Efron's percentile bootstrap, and bootstrap-t methods in both cases of the coverage probability and statistical power. It is interesting that this results are different from the intuitive expectations in view of the convergence rates of the resampling methods. The practical importance is also discussed for the distribution free Bagai statistic to test stochastic ordering.

Analyze Cervical Cancer Relapse Using Cox Proportional Hazards Model

양완연,하형태 한국자료분석학회 2009 Journal of the Korean Data Analysis Society Vol.11 No.5

Relapse and factors that affect relapse were analyzed using data on 905 cervical cancer patients by making use of Cox proportional hazards model. The period of this cervical cancer study was conducted from May 1984 to August 2001. Seven categorical and three continuous design variables were measured for each patient. For preliminary statistical analysis, seven design variables were found to be significant at 5% significance level. We reduced the number of variables via backward elimination method to find a survival model to best explain the cervix cancer relapse. The final survival model could be inferred that three factors, disease and depth and size of tumor, among ten design variables had most significant effects on cervix cancer relapse. Relapse rate functions of patients with large tumor were also smoothed.

Smartphone-based image analysis coupled to paper-based colorimetric devices

김다미,김세진,하형태,김상효 한국물리학회 2020 Current Applied Physics Vol.20 No.9

Advancements in technology have led to the use of smartphones as biosensor detectors. However, it is difficult to obtain stable color information of colorimetric sensors using multiple smartphones owing to different light conditions and image correction operations. In this study, we attempted color detection of the colorimetric paper chip using smartphone-embedded light-emitting diode (LED) and simple transformation calculation. This method enables the acquisition of stable color information using different smartphones by reducing the influence of external light sources. Moreover, we studied characteristics such as convergence and distinction of detection result details by the manufacturers and smartphones. These findings suggested the necessity of classification criteria for the use of smartphones to achieve optimal detection. In addition, white and black references were used to set the standard for color correction of various light sources. Based on our results, we conclude that this approach presents the possibility of smartphone-based colorimetric detection in practical applications.

The modified Mood test for the scale alternative and its numerical comparisons

Hidetoshi Murakami,하형태 한국통계학회 2015 Journal of the Korean Statistical Society Vol.44 No.4

On statistical hypotheses testing in two-sample problems, the Mood test is popular as one of the most efficient nonparametric tests for dispersion differences. In this paper, we show that a modification of the Mood test proposed by Tamura (1963) can gain even more efficiency and power under various distributional assumptions. The accuracy of the proposed approximations to the tail probabilities and critical values of the modified Mood test, namely Mp, were investigated. Our results showed that the Edgeworth expansion was more accurate than the other approximations. Asymptotic efficiencies and the optimal value p of the modified Mood test under various distributional assumptions were examined, with the results revealing that the large (small) value of p was useful for light (heavy) tail distributions. Additionally, the power of the modified Mood test for the one-sided alternative with various population distributions for small sample sizes was investigated via Monte Carlo simulations. Finally, the proposed method was demonstrated using real data.

On the Distribution of a Statistic Used for Detecting First-Order Serial Correlation

Deepak Sanjel,하형태,Serge B. Provost 한국자료분석학회 2008 Journal of the Korean Data Analysis Society Vol.10 No.1

This paper provides a simple methodology for approximating the distribution of a test statistic proposed by J. Durbin and G. S. Watson. After expressing the statistic as a ratio of quadratic forms, its exact moments are evaluated by making use of a recursive formula. Its density function is then approximated by a beta density function multiplied by a linear combination of Jacobi orthogonal polynomials. The coefficients of the linear combination are determined by making use of a moment-based methodology. An integral representation of the moments of the statistic under the alternative hypothesis is also provided. As verified by a simulation study, the approach used in this paper, which takes into account the observation matrix of explanatory variables associated with the assumed regression model, yields very accurate critical values for testing independence versus first-order serial correlation.

LG 마이크론의 품질과 생산성 향상을 위한 지적인 공정제어시스템 개발

조현보,전치혁,김광재,하형태,권치현,김영구 대한산업공학회 1999 ie 매거진 Vol.6 No.1

SADDLEPOINT APPROXIMATION TO GAMMA CONVOLUTIONS

YUN-HEE CHOI,조재린,MOGENS BLADT,하형태 장전수학회 2016 Proceedings of the Jangjeon mathematical society Vol.19 No.1

Gamma convolutions have been widely used in statistics and a wide range of scientic elds such as nance. Due to the difficulty of achieving analytically tractable expressions, the practical use of such models is limited. In this paper, we provide saddlepoint approxima- tions of gamma convolutions employing different saddlepoint approxi- mation methods|Daniels' (1954) and its normalized versions for den- sity approximation, and Lugannani and Rice's (1980) and its generalized (Wood et al., 1993) versions for cumulative distribution approximation. We examined their accuracies comparing to a simple gamma approx- imation recently proposed by Stewart et al. (2007) and numerically evaluated exact distribution (Sim, 1992) of gamma convolutions. Three illustrative examples demonstrate that the saddlepoint approximation techniques provide extremely accurate approximations to the exact dis- tributions of the gamma convolutions, especially to very small tail prob- abilities. R programming codes for the four versions of the saddlepoint approximation are provided in Appendix.