• Journal of the Korean Data and Information Science Society
• /
• v.18 no.3
• /
• pp.793-801
• /
• 2007

For multiply Type-II censored samples from a half-triangle distribution, the maximum likelihood method does not admit explicit solutions. In this case, we propose some explicit estimators of the location parameter in the half-triangle distribution by the approximate maximum likelihood methods. We compare the proposed estimators in the sense of the mean squared error for various censored samples.

• Communications for Statistical Applications and Methods
• /
• v.27 no.1
• /
• pp.97-108
• /
• 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.

• International Journal of Reliability and Applications
• /
• v.9 no.1
• /
• pp.31-52
• /
• 2008

In this paper generalized version of the geometric distribution is introduced. This distribution can be considered as a two-parameter generalization of the discrete geometric distribution. The main statistical and reliability properties of this distribution are discussed. Two methods of estimation, namely maximum likelihood method and the method of moments are used to estimate the parameters of this distribution. Simulation is utilized to calculate these estimates and to study some of their properties. Also, asymptotic confidence limits are established for the maximum likelihood estimates. Finally, the appropriateness of this new distribution for a set of real data, compared with the geometric distribution, is shown by using the likelihood ratio test and the Kolmogorove-Smirnove test.

• Communications for Statistical Applications and Methods
• /
• v.25 no.6
• /
• pp.647-658
• /
• 2018

In this paper, we study statistical inferences on the maximum likelihood estimation of a normal distribution when data are randomly censored. Likelihood equations are derived assuming that the censoring distribution does not involve any parameters of interest. The maximum likelihood estimators (MLEs) of the censored normal distribution do not have an explicit form, and it should be solved in an iterative way. We consider a simple method to derive an explicit form of the approximate MLEs with no iterations by expanding the nonlinear parts of the likelihood equations in Taylor series around some suitable points. The points are closely related to Kaplan-Meier estimators. By using the same method, the observed Fisher information is also approximated to obtain asymptotic variances of the estimators. An illustrative example is presented, and a simulation study is conducted to compare the performances of the estimators. In addition to their explicit form, the approximate MLEs are as efficient as the MLEs in terms of variances.

• Communications for Statistical Applications and Methods
• /
• v.30 no.2
• /
• pp.191-213
• /
• 2023

Unit distributions are frequently used in probability theory and statistics to depict meaningful variables having values between zero and one. Using convenient transformation, the unit inverse exponentiated weibull (UIEW) distribution, which is equally useful for modelling data on the unit interval, is proposed in this study. Quantile function, moments, incomplete moments, uncertainty measures, stochastic ordering, and stress-strength reliability are among the statistical properties provided for this distribution. To estimate the parameters associated to the recommended distribution, well-known estimation techniques including maximum likelihood, maximum product of spacings, least squares, weighted least squares, Cramer von Mises, Anderson-Darling, and Bayesian are utilised. Using simulated data, we compare how well the various estimators perform. According to the simulated outputs, the maximum product of spacing estimates has lower values of accuracy measures than alternative estimates in majority of situations. For two real datasets, the proposed model outperforms the beta, Kumaraswamy, unit Gompartz, unit Lomax and complementary unit weibull distributions based on various comparative indicators.

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

• International Journal of Reliability and Applications
• /
• v.13 no.2
• /
• pp.91-104
• /
• 2012

Sarhan and Kundu (2009) introduced a new distribution named as the generalized linear failure rate distribution. This distribution generalizes several well known distributions. The probability density function of the generalized linear failure rate distribution can be right skewed or unimodal and its hazard function can be increasing, decreasing or bathtub shaped. This distribution can be used quite effectively to analyze lifetime data in place of linear failure rate, generalized exponential and generalized Rayleigh distributions. In this paper, we apply the simulated annealing algorithm to obtain the maximum likelihood point estimates of the parameters of the generalized linear failure rate distribution. Simulated annealing algorithm can not only find the global optimum; it is also less likely to fail because it is a very robust algorithm. The estimators obtained using simulated annealing algorithm have been compared with the corresponding traditional maximum likelihood estimators for their risks.

• Magazine of the Korean Society of Agricultural Engineers
• /
• v.39 no.3
• /
• pp.83-95
• /
• 1997

This study was conducted to derive optimal design floods by Gamma distribution models of the annual maximum series at eight watersheds along Geum , Yeong San and Seom Jin river Systems, Design floods obtained by different methods for evaluation of parameters and for plotting positions in the Gamma distribution models were compared by the relative mean errors and graphical fit along with 95% confidence interval plotted on Gamma probability paper. The results were analyzed and summarized as follows. 1.Adequacy for the analysis of flood flow data used in this study was confirmed by the tests of Independence, Homogeneity and detection of Outliers. 2.Basic statistics and parameters were calculated by Gamma distribution models using Methods of Moments and Maximum Likelihood. 3.It was found that design floods derived by the method of maximum likelihood and Hazen plotting position formular of two parameter Gamma distribution are much closer to those of the observed data in comparison with those obtained by other methods for parameters and for plotting positions from the viewpoint of relative mean errors. 4.Reliability of derived design floods by both maximum likelihood and method of moments with two parameter Gamma distribution was acknowledged within 95% confidence interval.

• KEPCO Journal on Electric Power and Energy
• /
• v.7 no.1
• /
• pp.171-177
• /
• 2021

In terms of distribution planning, accurate electric load prediction is one of the most important factors. The future load prediction has manually been performed by calculating the maximum electric load considering loads transfer/switching and multiplying it with the load increase rate. In here, the risk of human error is inherent and thus an automated maximum electric load forecasting system is required. Although there are many existing methods and techniques to predict future electric loads, such as regression analysis, many of them have limitations in reflecting the nonlinear characteristics of the electric load and the complexity due to Photovoltaics (PVs), Electric Vehicles (EVs), and etc. This study, therefore, proposes a method of predicting future electric loads on distribution lines by using Machine Learning (ML) method that can reflect the characteristics of these nonlinearities. In addition, predictive models were developed based on actual data collected at KEPCO's existing distribution lines and the adequacy of developed models was verified as well. Also, as the distribution planning has a direct bearing on the investment, and amount of investment has a direct bearing on the maximum electric load, various baseline such as maximum, lowest, median value that can assesses the adequacy and accuracy of proposed ML based electric load prediction methods were suggested.

• Journal of Environmental Science International
• /
• v.30 no.12
• /
• pp.983-991
• /
• 2021

The role of the distribution basin role is to apportion incoming raw water to the primary sedimentation basin as part of the water treatment process. The purpose of this study was to calculate the amount of water in the distribution basin using computational fluid dynamics (CFD) analysis and to find a way to improve any non-uniformity. We used the Taguchi method and the minitab tool as optimization methods. The results of the CFD calculation showed that the distribution flow had a deviation of 5% at the minimum inflow, 10% at the average inflow, and 22% at the maximum inflow. At maximum flow, the appropriate heights of the 7 weirs(C, D, A, B, E, F, G) were 40 mm, 20 mm, 20 mm, 0, 0, 0, and 20 mm, respectively, according to the Taguchi optimization tool. Here, the maximum deviation of the distribution amount was 9% and the standard deviation was 23.7. The appropriate heights of the 7 weirs, according to the Minitab tool, were 40 mm, 20 mm, 20 mm, 0, 0, 0, and 20 mm, respectively, for weirs C, D, A, B, E, F, and G. Therefore, the maximum deviation of the distribution amount was 8% and the standard deviation was 17.1, which was slightly improved compared to the Taguchi method.