• Communications for Statistical Applications and Methods
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• v.26 no.5
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• pp.473-495
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• 2019

In this paper, a new extension of Lindley distribution has been introduced. Certain characterizations based on truncated moments, hazard and reverse hazard function, conditional expectation of the proposed distribution are presented. Besides, these characterizations, other statistical/mathematical properties of the proposed model are also discussed. The estimation of the parameters is performed through different classical methods of estimation. Bayes estimation is computed under gamma informative prior under the squared error loss function. The performances of all estimation methods are studied via Monte Carlo simulations in mean square error sense. The potential of the proposed model is analyzed through two data sets. A modified goodness-of-fit test using the Nikulin-Rao-Robson statistic test is investigated via two examples and is observed that the new extension might be used as an alternative lifetime model.

• 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.

• 한국데이터정보과학회:학술대회논문집
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• 2006.04a
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• pp.163-169
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• 2006

This paper deals with the comparison of parameter estimation methods in a 3-parameter Kappa distribution which is sometimes used in flood frequency analysis. The method of moment estimation(MME), L-moment estimation(L-ME), and maximum likelihood estimation(MLE) are applied to estimate three parameters. The performance of these methods are compared by Monte-carlo simulations. Especially for computing MME and L-ME, ike dimensional nonlinear equations are simplied to one dimensional equation which is calculated by the Newton-Raphson iteration under constraint. Based on the criterion of the mean squared error, the L-ME is recommended to use for small sample size $(n\leq100)$ while MLE is good for large sample size.

• Communications for Statistical Applications and Methods
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• v.3 no.2
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• pp.37-42
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• 1996

Maximum likelihood estimation of Cholesky decomposition is considered under normality assumption. It is shown that maximum liklihood estimation gives a Cholesky decomposition of the sample covariance matrix. The joint distribution of the maximum likelihood estimators is derived. The ussual algorithm for a Cholesky decomposition is shown to be equivalent to a maximumlikelihood estimation of a Cholesky root when the underlying distribution is a multivariate normal one.

• Journal of Information Processing Systems
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• v.15 no.4
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• pp.820-832
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• 2019

Estimation of accurate blood volume flow in ultrasound Doppler blood flow spectrograms is extremely important for clinical diagnostic purposes. Blood volume flow measurements require the assessment of both the velocity distribution and the cross-sectional area of the vessel. Unfortunately, the existing volume flow estimation algorithms by ultrasound lack the velocity space distribution information in cross-sections of a vessel and have the problems of low accuracy and poor stability. In this paper, a new robust ultrasound volume flow estimation method based on multigate (RMG) is proposed and the multigate technology provides detail information on the local velocity distribution. In this method, an accurate double iterative flow velocity estimation algorithm (DIV) is used to estimate the mean velocity and it has been tested on in vivo data from carotid. The results from experiments indicate a mean standard deviation of less than 6% in flow velocities when estimated for a range of SNR levels. The RMG method is validated in a custom-designed experimental setup, Doppler phantom and imitation blood flow control system. In vitro experimental results show that the mean error of the RMG algorithm is 4.81%. Low errors in blood volume flow estimation make the prospect of using the RMG algorithm for real-time blood volume flow estimation possible.

• Communications for Statistical Applications and Methods
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• v.24 no.3
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• pp.227-240
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• 2017

In this paper, we introduce the inverted exponentiated Weibull (IEW) distribution which contains exponentiated inverted Weibull distribution, inverse Weibull (IW) distribution, and inverted exponentiated distribution as submodels. The proposed distribution is obtained by the inverse form of the exponentiated Weibull distribution. In particular, we explain that the proposed distribution can be interpreted by Marshall and Olkin's book (Lifetime Distributions: Structure of Non-parametric, Semiparametric, and Parametric Families, 2007, Springer) idea. We derive the cumulative distribution function and hazard function and calculate expression for its moment. The hazard function of the IEW distribution can be decreasing, increasing or bathtub-shaped. The maximum likelihood estimation (MLE) is obtained. Then we show the existence and uniqueness of MLE. We can also obtain the Bayesian estimation by using the Gibbs sampler with the Metropolis-Hastings algorithm. We also give applications with a simulated data set and two real data set to show the flexibility of the IEW distribution. Finally, conclusions are mentioned.

• Journal of Wetlands Research
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• v.16 no.1
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• pp.103-112
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• 2014

Area average rainfall estimation is important to determine the exact amount of the available water resources and the essential input data for rainfall-runoff analysis. Like that, the necessary criterion for accurate area average rainfall estimate is the uniform spatial distribution of raingauge network. In this study, we suggest the spatial distribution evaluation methodology of raingauge network to estimate better area average rainfall and after the suggested method is applied to Han River and Geum River basin. The spatial distribution of rainfall network can be quantified by the nearest neighbor index. In order to evaluate the effects of the spatial distribution of rainfall network by each basin, area average rainfall was estimated by arithmetic mean method, the Thiessen's weighting method and estimation theory for 2013's rainfall event, and evaluated the involved errors by each cases. As a result, it can be found that the estimation error at the best basin of spatial distribution was lower than the worst basin of spatial distribution.

• 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.

• Journal of Korean Society of Forest Science
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• v.59 no.1
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• pp.46-50
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• 1983

Estimation of stand diameter distribution by using Weibull distribution, and then the result is tested by Kolomogorov-Smirnov method expresses very fine fitted.

• International Journal of Reliability and Applications
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• v.3 no.1
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• pp.51-60
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• 2002

This paper presents the methodology for obtaining point and interval estimating of the parameters of a new two-parameter distribution with multiple-censored and singly censored data (Type-I censoring or Type-II censoring) as well as complete data, using the maximum likelihood method. The basis is the likelihood expression for multiple-censored data. Furthermore, this model can be extended to a three-parameter distribution that is added a scale parameter. Then, the parameter estimation can be obtained by the graphical estimation on probability plot.