• Communications for Statistical Applications and Methods
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• v.27 no.4
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• pp.469-486
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• 2020

Entropy is an important term in statistical mechanics that was originally defined in the second law of thermodynamics. In this paper, we consider the maximum likelihood estimation (MLE), maximum product spacings estimation (MPSE) and Bayesian estimation of the entropy of an inverse Weibull distribution (InW) under a generalized type I progressive hybrid censoring scheme (GePH). The MLE and MPSE of the entropy cannot be obtained in closed form; therefore, we propose using the Newton-Raphson algorithm to solve it. Further, the Bayesian estimators for the entropy of InW based on squared error loss function (SqL), precautionary loss function (PrL), general entropy loss function (GeL) and linex loss function (LiL) are derived. In addition, we derive the Lindley's approximate method (LiA) of the Bayesian estimates. Monte Carlo simulations are conducted to compare the results among MLE, MPSE, and Bayesian estimators. A real data set based on the GePH is also analyzed for illustrative purposes.

• Water Engineering Research
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• v.4 no.3
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• pp.155-173
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• 2003

Parameters and quantiles of the 2-parameter generalized Pareto distribution were estimated using the methods of regular moments, modified moments, probability weighted moments, linear moments, maximum likelihood, and entropy for Monte Carlo-generated samples. The performance of these seven estimators was statistically compared, with the objective of identifying the most robust estimator. It was found that in general the methods of probability-weighted moments and L-moments performed better than the methods of maximum likelihood estimation, moments and entropy, especially for smaller values of the coefficient of variation and probability of exceedance.

• Journal of the Korean Data and Information Science Society
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• v.28 no.3
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• pp.659-668
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• 2017

The inverse Weibull distribution (IWD) can be readily applied to a wide range of situations including applications in medicines, reliability and ecology. It is generally known that the lifetimes of test items may not be recorded exactly. In this paper, therefore, we consider the maximum likelihood estimation (MLE) and Bayes estimation of the entropy of a IWD under generalized progressive hybrid censoring (GPHC) scheme. It is observed that the MLE of the entropy cannot be obtained in closed form, so we have to solve two non-linear equations simultaneously. Further, the Bayes estimators for the entropy of IWD based on squared error loss function (SELF), precautionary loss function (PLF), and linex loss function (LLF) are derived. Since the Bayes estimators cannot be obtained in closed form, we derive the Bayes estimates by revoking the Tierney and Kadane approximate method. We carried out Monte Carlo simulations to compare the classical and Bayes estimators. In addition, two real data sets based on GPHC scheme have been also analysed for illustrative purposes.

• Communications for Statistical Applications and Methods
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• v.21 no.5
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• pp.395-409
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• 2014

Data limited, partial, or incomplete are known as an ill-posed problem. If the data with ill-posed problems are analyzed by traditional statistical methods, the results obviously are not reliable and lead to erroneous interpretations. To overcome these problems, we propose a dual generalized maximum entropy (dual GME) estimator for panel data regression models based on an unconstrained dual Lagrange multiplier method. Monte Carlo simulations for panel data regression models with exogeneity, endogeneity, or/and collinearity show that the dual GME estimator outperforms several other estimators such as using least squares and instruments even in small samples. We believe that our dual GME procedure developed for the panel data regression framework will be useful to analyze ill-posed and endogenous data sets.

• Communications for Statistical Applications and Methods
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• v.24 no.4
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• pp.353-365
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• 2017

In this article, we proposed a new three-parameter distribution called generalized half-logistic Poisson distribution with a failure rate function that can be increasing, decreasing or upside-down bathtub-shaped depending on its parameters. The new model extends the half-logistic Poisson distribution and has exponentiated half-logistic as its limiting distribution. A comprehensive mathematical and statistical treatment of the new distribution is provided. We provide an explicit expression for the $r^{th}$ moment, moment generating function, Shannon entropy and $R{\acute{e}}nyi$ entropy. The model parameter estimation was conducted via a maximum likelihood method; in addition, the existence and uniqueness of maximum likelihood estimations are analyzed under potential conditions. Finally, an application of the new distribution to a real dataset shows the flexibility and potentiality of the proposed distribution.

• Communications for Statistical Applications and Methods
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• v.16 no.4
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• pp.659-667
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• 2009

Recently Song and Cheon (2006) and Cheon and Lim (2009) developed the generalized maximum entropy(GME) estimator to solve ill-posed problems for the regression coefficients in the simple panel model. The models discussed consider the individual and a spatial autoregressive disturbance effects. However, in many application in economics the data may contain nested groupings. This paper considers a two-way error component model with nested groupings for the ill-posed data and proposes the GME estimator of the unknown parameters. The performance of this estimator is compared with the existing methods on the simulated dataset. The results indicate that the GME method performs the best in estimating the unknown parameters in terms of its quality when the data are ill-posed.

• Communications for Statistical Applications and Methods
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• v.9 no.1
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• pp.13-19
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• 2002

In nonparametric entropy estimation, both mass and mean-preserving maximum entropy distribution (Theil, 1980) and the underlying distribution of the sample entropy (Vasicek, 1976), the most widely used entropy estimator, consist of nb mass-preserving densities based on disjoint Intervals of the simple averages of two adjacent order statistics. In this paper, we notice that those nonparametric density functions do not actually keep the mass-preserving constraint, and propose a modified sample entropy by considering the generalized 0-statistics (Kaigh and Driscoll, 1987) in averaging two adjacent order statistics. We consider the proposed estimator in a goodness of fit test for normality and compare its performance with that of the sample entropy.

• The Korean Journal of Applied Statistics
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• v.19 no.3
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• pp.521-534
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• 2006

This paper considers a panel regression model with ill-posed data and proposes the generalized maximum entropy(GME) estimator of the unknown parameters. These are natural extensions from the biometries, statistics and econometrics literature. The performance of this estimator is investigated by using of Monte Carlo experiments. The results indicate that the GME method performs the best in estimating the unknown parameters.

• Communications for Statistical Applications and Methods
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• v.16 no.2
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• pp.265-275
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• 2009

This paper considers a linear regression model with a spatial autoregressive disturbance with ill-posed data and proposes the generalized maximum entropy(GME) estimator of regression coefficients. The performance of this estimator is investigated via Monte Carlo experiments. The results show that the GME estimator provides efficient and robust estimate for the unknown parameter.

• Journal of the Korean Data and Information Science Society
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• v.26 no.2
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• pp.535-545
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• 2015

In a various range of applications including hydrology, the type-I extreme value distribution has been extensively used as a probabilistic model for analyzing extreme events. In this paper, we introduce methods for estimating the scale parameter of the type-I extreme value distribution. A simulation study is performed to compare the estimators in terms of mean-squared error and bias, and the obtained results are provided.