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General cumulative Kullback-Leibler information
Park, Sangun,Noughabi, Hadi Alizadeh,Kim, Ilmun Informa UK (TaylorFrancis) 2018 Communications in Statistics Vol.47 No.7
<P>The cumulative residual Kullback-Leibler information is defined on the semi-infinite (non negative) interval. In this paper, we extend the cumulative residual Kullback-Leibler information to the whole real line and propose a general cumulative Kullback-Leibler information. We study its application to a test for normality in comparison with some competing test statistics based on the empirical distribution function including the well-known tests applied in practice like Kolmogorov-Smirnov, Cramer-von Mises, Anderson-Darling, and other existing tests.</P>
Fisher Information in Statistical Theory and Models
Park, Sangun 延世大學校經濟硏究所 1996 延世經濟硏究 Vol.3 No.2
We summarize some topics in the present statistical theory and discuss over the role of the Fisher information in those topice. We first study some measures of information and their roles in statistics. Then we look over the data reduction and the loss of information due to the reduction. We interpret some present statistical arguments on point and interval estimation in terms of the Fisher information. We further comment on some statistical models related with the Fisher information.
On the comparison of cumulative hazard functions
Park, Sangun,Ha, Seung Ah The Korean Statistical Society 2019 Communications for statistical applications and me Vol.26 No.6
This paper proposes two distance measures between two cumulative hazard functions that can be obtained by comparing their difference and ratio, respectively. Then we estimate the measures and present goodness of t test statistics. Since the proposed test statistics are expressed in terms of the cumulative hazard functions, we can easily give more weights on earlier (or later) departures in cumulative hazards if we like to place an emphasis on earlier (or later) departures. We also show that these test statistics present comparable performances with other well-known test statistics based on the empirical distribution function for an exponential null distribution. The proposed test statistic is an omnibus test which is applicable to other lots of distributions than an exponential distribution.
A general class of flexible Weibull distributions
Park, Sangun,Park, Jiwhan Informa UK (TaylorFrancis) 2018 Communications in Statistics Vol.47 No.4
<P>We consider a linear combination of two logarithms of cumulative hazard functions and propose a general class of flexible Weibull distribution functions which includes some well-known modified Weibull distributions (MWDs). We suggest a very flexible Weibull distribution, which belongs to the class, and show that its hazard function is monotone, bathtub-shaped, modified bathtub-shaped, or even upside-down bathtub-shaped. We also discuss the methods of least square estimation and maximum likelihood estimation of the unknown parameters. We take two illustrated examples to compare the suggested distribution with some current MWDs, and show that the suggested distribution shows good performances.</P>
Generalized Kullback-Leibler information and its extensions to censored and discrete cases
Park, Sangun The Korean Data and Information Science Society 2012 한국데이터정보과학회지 Vol.23 No.6
In this paper, we propose a generalized Kullback-Leibler (KL) information for measuring the distance between two distribution functions where the extension to the censored case is immediate. The generalized KL information has the nonnegativity and characterization properties, and its censored version has the additional property of monotonic increase. We also extend the discussion to the discrete case and propose a generalized censored measure which is comparable to Pearson's chi-square statistic.
Park, Sangun,Choi, Dongseok,Jung, Sangah The Korean Statistical Society 2014 Communications for statistical applications and me Vol.21 No.2
Kullback-Leibler (KL) information is a measure of discrepancy between two probability density functions. However, several nonparametric density function estimators have been considered in estimating KL information because KL information is not well-defined on the empirical distribution function. In this paper, we consider the KL information of the equilibrium distribution function, which is well defined on the empirical distribution function (EDF), and propose an EDF-based goodness of fit test statistic. We evaluate the performance of the proposed test statistic for an exponential distribution with Monte Carlo simulation. We also extend the discussion to the censored case.