• Kyungpook Mathematical Journal
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• v.55 no.2
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• pp.335-344
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• 2015

In the paper we discuss the value distribution of the product of the derivative of a transcendental meromorphic function and a power of the function.

• Communications for Statistical Applications and Methods
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• v.31 no.1
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• pp.129-142
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• 2024

In various industries, especially manufacturing and chemical industries, it is often observed that the distribution of a specific process, initially having followed a normal distribution, becomes skewed as a result of unexpected causes. That is, a process deviates from a normal distribution and becomes a skewed distribution. The skew-normal (SN) distribution is one of the most employed models to characterize such processes. The shape of this distribution is determined by the asymmetry parameter. When this parameter is set to zero, the distribution is equal to the normal distribution. Moreover, when there is a shift in the asymmetry parameter, the mean and variance of a SN distribution shift accordingly. In this paper, we propose procedures for monitoring the asymmetry parameter, based on the statistic derived from the noncentral t-distribution. After applying the statistic to Shewhart and the exponentially weighted moving average (EWMA) charts, we evaluate the performance of the proposed procedures and compare it with previously studied procedures based on other skewness statistics.

• Journal of the Korean Data and Information Science Society
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• v.21 no.5
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• pp.967-972
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• 2010

We shall consider estimations of an exponetiated parameter of the exponentiated Pareto distribution with known scale and threshold parameters. A quotient distribution of two independent exponentiated Pareto random variables is obtained. We also derive the distribution of the ratio of two independent exponentiated Pareto random variables.

• Journal of applied mathematics & informatics
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• v.41 no.2
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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 Distribution Science
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• v.19 no.4
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• pp.53-60
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• 2021

Purpose: This study focuses on exploring ways to improve the distribution method of shrimp farming so that it is eco-friendly and increases the distribution of shrimp. Research design, data and methodology: The experimental device installed in a biofloc shrimp culture in one area tested 10 times. Complex odor, concentration of H2S, water quality improvement effected by decomposition of organic substances, and degree of microbial activation measured. The data of the experimental results verified using the T-test technique, and the p value was determined based on the significance probability of 0.05. Results: This experimental device was effective in reducing odor and hydrogen sulfide in shrimp farms. With the improvement of water quality, dissolved oxygen increased due to the microbubble and cavitation action of air ejector and ultrasonic waves. In addition, the cultured microorganisms in the cultured water treated by the experimental device were remarkably proliferated compared to the raw water. Conclusions: The biofloc distribution method has a significant effect on improving water quality and reducing odor substances and will become a new eco-friendly and efficient distribution method for shrimp farming in the future.

• Communications for Statistical Applications and Methods
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• v.24 no.3
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• pp.193-209
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• 2017

The power Lindley distribution with some of its properties is considered in this article. Maximum likelihood, least squares, maximum product spacings, and Bayes estimators are proposed to estimate all the unknown parameters of the power Lindley distribution. Lindley's approximation and Markov chain Monte Carlo techniques are utilized for Bayesian calculations since posterior distribution cannot be reduced to standard distribution. The performances of the proposed estimators are compared based on simulated samples. The waiting times of research articles to be accepted in statistical journals are fitted to the power Lindley distribution with other competing distributions. Chi-square statistic, Kolmogorov-Smirnov statistic, Akaike information criterion and Bayesian information criterion are used to access goodness-of-fit. It was found that the power Lindley distribution gives a better fit for the data than other distributions.

• International Journal of Reliability and Applications
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• v.17 no.1
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• pp.1-19
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• 2016

The Exponentiated Quasi Lindley (EQL) distribution which is an extension of the quasi Lindley Distribution is introduced and its properties are explored. This new distribution represents a more flexible model for the lifetime data. Some statistical properties of the proposed distribution including the shapes of the density and hazard rate functions, the moments and moment generating function, the distribution of the order statistics are given. The maximum likelihood estimation technique is used to estimate the model parameters and finally an application of the model with a real data set is presented for the illustration of the usefulness of the proposed distribution.

• Journal of the Korean Data and Information Science Society
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• v.26 no.2
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• pp.313-322
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• 2015

A mixture distribution of a discrete uniform or degenerated distribution and two binomial distribution is proposed and a method of obtaining the maximum likelihood estimates of the parameters is provided. For the proposed model simulation studies were conducted to see performance of the maximum likelihood estimates and a mixture of a degenerated distribution and two binomial distributions was applied to fit a lecture evaluation data to show a good result.

• Journal of Information Display
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• v.12 no.4
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• pp.167-171
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• 2011

The angular distribution of the luminance on each optical component of 40-inch light-emitting diode backlight was measured and studied, using the optical-simulation method. Several scattering functions were investigated as the reflection distribution function of the scattering dots printed on the bottom surface of the light guide plate (LGP). It was found that both the diffuse Lambertian and near-specular Gaussian scattering functions were necessary for the successful reproduction of the experimental angular distribution of the luminance. The optimization of the scattering parameters included in these scattering functions led to almost the same luminance distribution as that obtained from the experiment. This approach may be an effective way of indirectly estimating the reflection distribution function of the scattering dots of the LGP, which cannot be made accessible through any other experimental method.

• Journal of the Korean Statistical Society
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• v.30 no.3
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• pp.467-480
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• 2001

This paper considers the use of local $\phi$-divergence measures between posterior distributions under classes of perturbations in order to investigate the inherent robustness of certain classes. The smaller value of the limiting local $\phi$-divergence implies more robustness for the prior or the likelihood. We consider the cases when the likelihood comes form the class of weighted distribution. Two kinds of perturbations are considered for the local sensitivity analysis. In addition, some numerical examples are considered which provide measures of robustness.