• Communications for Statistical Applications and Methods
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• 제27권1호
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• pp.97-108
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• 2020

This paper compares several methods for estimating parameters of normal inverse Gaussian distribution. Ordinary maximum likelihood estimation and the method of moment estimation often do not work properly due to restrictions on parameters. We examine the performance of adjusted estimation methods along with the ordinary maximum likelihood estimation and the method of moment estimation by simulation and real data application. We also see the effect of the initial value in estimation methods. The simulation results show that the ordinary maximum likelihood estimator is significantly affected by the initial value; in addition, the adjusted estimators have smaller root mean square error than ordinary estimators as well as less impact on the initial value. With real datasets, we obtain similar results to what we see in simulation studies. Based on the results of simulation and real data application, we suggest using adjusted maximum likelihood estimates with adjusted method of moment estimates as initial values to estimate the parameters of normal inverse Gaussian distribution.

• Communications for Statistical Applications and Methods
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• 제30권4호
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• pp.411-421
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• 2023

This paper provides a new estimation equation based on the concept of a minimum distance between the empirical and theoretical distribution functions under the most widely used progressive Type-II censoring scheme. For illustrative purposes, simulated and real datasets from a three-parameter Weibull distribution are analyzed. For comparison, the most popular estimation methods, the maximum likelihood and maximum product of spacings estimation methods, are developed together. In the analysis of simulated datasets, the excellence of the provided estimation method is demonstrated through the degree of the estimation failure of the likelihood-based method, and its validity is demonstrated through the mean squared errors and biases of the estimators obtained from the provided estimation equation. In the analysis of the real dataset, two types of goodness-of-fit tests are performed on whether the observed dataset has the three-parameter Weibull distribution under the progressive Type-II censoring scheme, through which the performance of the new estimation equation provided is examined.

• Journal of Oral Medicine and Pain
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• 제43권4호
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• pp.118-124
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• 2018

Purpose: Age estimation is often used in the identification of living persons. Various methods are used for age estimation using teeth, and there are many studies on the methodology. But the study of changes in the social aspects of age estimation with the passage of times is still insufficient. Therefore, the purpose of this study is to analyze the age estimation cases in the social aspects and to investigate the changes of age estimation cases in Jeollabuk-do. Methods: From January 2008 to December 2015, 76 cases of age estimation were collected. The collected data were organized and analyzed. The distribution of patients by age and year, the difference between alleged and registered age, the purpose of age estimation, and regional distribution were examined. In addition, we compared the previous study which analyzed the age estimation cases in Jeollabuk-do from 2000 to 2007. Results: According to the distribution by age, the age distribution was the largest in the 50s and 60s, with 69.8%. The most reason to correct age was related to welfare benefits (38.2%), and most of the people who corrected for welfare benefits were over 50 years old. The age correction for purpose of welfare benefits existed every year during the study period. As the result of comparison with previous study, total number of age estimation cases was decreased very sharply, and distribution by age group was also changed. Conclusions: Changes in age estimation cases were observed when compared to the previous study. A significant decrease in the total number of age estimation cases was observed, but the number of age estimation in the 50s did not decrease. Although the total number of age estimation requests decreases, age estimation in the elderly are likely to persist. Thus, it is necessary to study new age estimation methods suitable for the elderly.

• 대한산업공학회지
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• 제42권4호
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• pp.256-262
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• 2016

The Weibull is widely used in reliability analysis, and several studies have attempted to improve estimation of the distribution's parameters. least squares estimation (LSE) or Maximum likelihood estimation (MLE) are often used to estimate distribution parameters. However, it has been proven that Bayesian methods are more suitable for small sample sizes than LSE and MLE. In this work, the Weibull parameter estimation accuracy of LSE, MLE, and Bayesian method are compared for sample sets with 3 to 30 data points. The Bayesian method was most accurate for sample sizes under 25, and the accuracy of the Bayesian method was similar to LSE and MLE as the sample size increased.

• 전기학회논문지
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• 제61권8호
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• pp.1083-1090
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• 2012

In this paper, we present the section load estimation program of distribution system for smart distribution management system. The proposed program is composed with three parts. One is the consistency check part for switch measurements which consist a section. The consistency check is divided into the current and angle test. For the current test, we examine the input and output power flow for the switch group. For the angle test, the result of power flow calculation at previous step is used. Another is the voltage estimation part for the measured switches. We use the weighted least square (WLS) method for the voltage estimation. The third is the part of final section load calculation. The database structure for accomplishing the developed estimation program is also proposed. To verify the accuracy of the experimental results, case studies are performed using a actual data of Jeju island. The developed program can be effectively applied to the distribution operation systems.

• 대한교통학회지
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• 제30권5호
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• pp.43-59
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• 2012

통행분포 예측시 목표년도가 단기일 경우에는 성장인자모형의 예측 정확도가 높고, 장기 목표년도의 경우에는 중력모형의 예측 정확도가 높은 것으로 인식되어 오고 있다. 이와 같은 예측모형 적용경향에 대한 검정을 위해 본 연구에서는 대구시 3개 년도(1988년, 1992년, 2004년)의 O-D표를 이용하여 통행분포 예측모형들의 정확도를 비교하였다. 비교는 분석 죤이 대죤인 경우와 중죤인 경우에서 예측모형별로 단기 목표년도의 정확도와 장기 목표년도 정확도를 구분하여 행하였다. 비교결과, 통행분포 예측모형의 통상적인 인식과 다른 결과가 있을 수 있다는 것이 규명되었다.

• Journal of applied mathematics & informatics
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• 제41권2호
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• pp.449-468
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• 2023

This paper deals in the study of the estimation of the parameters of Erlang distribution based on rank set sampling and some of its modifications. Here we considered Maximum Likelihood (ML) and the Bayesian technique to estimate the shape and scale parameter of Erlang distribution based on RSS and its some modifications such as ERSS, MRSS, and MRSSu. The derivation for unknown parameters of Erlang distribution is well presented using normal approximation to the asymptotic distribution of ML estimators. But due to the complexity involves in the integral, the Bayes estimator of unknown parameters is obtained using MCMC method. Further, we compared the MSE of estimation in different sampling schemes with different set sizes and cycle size. A real-life data application is also given to illustrate the efficiency of the proposed scheme.

• Journal of the Korean Statistical Society
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• 제32권3호
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• pp.289-298
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• 2003

We consider the estimation problem for the scale parameter of the Rayleigh distribution using weighted balanced loss function (WBLF) which reflects both goodness of fit and precision. Under WBLF, we obtain the optimal estimator which creates a kind of balance between Bayesian and non-Bayesian estimation. We also deal with the estimation of R ＝ P(Y < X) when Y and X are two independent but not identically distributed Rayleigh distribution under squared error loss function.

• Communications for Statistical Applications and Methods
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• 제21권2호
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• pp.147-160
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• 2014

In this paper, we introduce the exponentiated Weibull-geometric (EWG) distribution which generalizes two-parameter exponentiated Weibull (EW) distribution introduced by Mudholkar et al. (1995). This proposed distribution is obtained by compounding the exponentiated Weibull with geometric distribution. We derive its cumulative distribution function (CDF), hazard function and the density of the order statistics and calculate expressions for its moments and the moments of the order statistics. The hazard function of the EWG distribution can be decreasing, increasing or bathtub-shaped among others. Also, we give expressions for the Renyi and Shannon entropies. The maximum likelihood estimation is obtained by using EM-algorithm (Dempster et al., 1977; McLachlan and Krishnan, 1997). We can obtain the Bayesian estimation by using Gibbs sampler with Metropolis-Hastings algorithm. Also, we give application with real data set to show the flexibility of the EWG distribution. Finally, summary and discussion are mentioned.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제12권3호
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• pp.153-160
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• 2008

A size-biased Poisson distribution is defined. Its characterization by using a recurrence relation for first order negative moment of the distribution is obtained. Different estimation methods for the parameter of the model are also discussed. R-Software has been used for making a comparison among the three different estimation methods.