Sang-eon Park

Calculation of the entropy of a set of consecutive order statistics is relatively more complicated than that of the entropy of the individual order statistic, which has been studied by Wong and Chan (1990). We provide some fundamental relations occurring in the entropy of consecutive-order statistics, which are very useful for computations. We first consider the decomposition of the entropy of order statistics, and derive some recurrence relations in the first r order statistics. We also establi

The sample entropy (Vasicek, 1976) has been most widely used as a nonparametric entropy estimator due to its simplicity, but its underlying distribution function has not been known yet though its moments are required in establishing the entropy-based goodness of test statistic (Soofi et al., 1995). In this paper we derive the nonparametric distribution function of the sample entropy as a piece-wise uniform distribution in the lights of Theil (1980) and Dudwicz and van der Meulen (1987). Then we

Abstract When we have n independently and identically distributed observations, it is an interesting question how the Fisher information is distributed among order statistics. The recipe for the Fisher information in order statistics is easy, but the detailed calculation has been known to be complicated. An indirect approach, using a decomposition of the Fisher information in order statistics, simplifies the calculation. Some recurrence relations for the Fisher information in order statistics ar

The Kulback-Leibler information has been considered for establishing goodness-of-fit test statistics, which have been shown to perform very well (Arizono & Ohta, 1989; Ebrahimi et al., 1992, etc). In this paper, we propose censored Kullback-Leibler information to generalize the discussion of the Kullback-Leibler information to the censored case. Then we establish a goodness-of-fit test statistic based on the censored Kullback-Leibler information with the type 2 censored data, and compare the tes

In this paper, we study the Kullback–Leibler (KL) information of a censored variable, which we will simply call it censored KL information. The censored KL information is shown to have the necessary monotonicity property in addition to inherent properties of nonnegativity and characterization. We also present a representation of the censored KL information in terms of the relative risk and study its relation with the Fisher information in censored data. Finally, we evaluate the estimated censore

Abstract When we have n independently and identically distributed observations, it is an interesting question how the Fisher information is distributed among order statistics. The recipe for the Fisher information in order statistics is easy, but the detailed calculation has been known to be complicated. An indirect approach, using a decomposition of the Fisher information in order statistics, simplifies the calculation. Some recurrence relations for the Fisher information in order statistics ar

Various hybrid censoring schemes, which are mixtures of Type I and Type II censoring schemes, have been suggested for flexibility in termination time and efficiency level. In this paper, we propose a general hybrid censoring scheme to be a censoring scheme with Type I or Type II bounds which provides more flexible termination time and efficiency level. The Type I hybrid censoring scheme can be interpreted as a Type I censoring scheme with a Type II upper bound, while the generalized Type I hybri