• Journal of the Korean Data and Information Science Society
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• v.8 no.1
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• pp.59-70
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• 1997

We introduce several estimators of the location and the scale parameters of the two-parameter exponential distribution, and then compare these estimators by the mean square error (MSE). Using the parametric bootstrap estimators and the delete-d jackknife, we obtain the bootstrap and the delete-d jackknife confidence intervals for the location and the scale parameters and compare the bootstrap confidence intervals with the delete-d jackknife confidence intervals by length and coverage probability through Monte Carlo method.

• Communications for Statistical Applications and Methods
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• v.20 no.4
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• pp.241-246
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• 2013

In this study, we propose a nonparametric simultaneous test procedure for the location translation and scale parameters. We consider the Wilcoxon rank sum test for the location translation parameter and the Mood test for the scale parameter with the quadratic and maximal types of combining functions. Then we derive the limiting null distributions of the combining functions. We illustrate our procedure with an example and compare efficiency by obtaining the empirical powers through a simulation study. Finally, we discuss some interesting features related to the nonparametric simultaneous tests.

• The Korean Journal of Applied Statistics
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• v.4 no.2
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• pp.129-135
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• 1991

A few simple methods to find $L_1$-unbiased estimators for location and scale parameters are summarized and examples utilizing diffusivity, a natural measure of dispersion for $L_1$-unbiased estimators, are given.

• Communications for Statistical Applications and Methods
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• v.14 no.2
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• pp.329-344
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• 2007

In this paper, we shall propose the AMLEs of the scale parameter and the location parameter in the two-parameter Rayleigh distribution based on progressive Type-II censored samples when one parameter is known. We also propose the AMLEs of the two parameters in the Rayleigh distribution based on progressive Type-II censored samples when two parameters are unknown. We simulate the mean squared errors of the proposed estimators through Monte Carlo simulation for various censoring schemes.

• Communications for Statistical Applications and Methods
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• v.9 no.1
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• pp.221-227
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• 2002

The concept of pivot has been widely used in various classical inferences. In this paper, it is proved by use of pivotal quantities that the Bayesian inferences can be arrived at the same results of classical inferences for the location-scale parameters models under the assumption of non-informative prior distributions. Some theorems are proposed in which the posterior distribution and the sampling distribution of a pivotal quantity coincide. The theorems are applied illustratively to some statistical models.

• Communications for Statistical Applications and Methods
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• v.12 no.3
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• pp.603-613
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• 2005

We propose some estimators of the location parameter and derive the approximate maximum likelihood estimators (AMLEs) of the scale parameter in the exponential distribution based on multiply Type-II censored samples. We calculate the moments for the proposed estimators of the location parameter, and the AMLEs which are the linear functions of the order statistics. We compare the proposed estimators in the sense of the mean squared error (MSE) for various censored samples.

• Journal of the Korean Data and Information Science Society
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• v.15 no.1
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• pp.227-237
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• 2004

In this paper we presented a Bayesian inference approach for estimating the location and scale parameters of the lognormal distribution using iterative Gibbs sampling algorithm. We also presented estimation of location parameter by two non iterative methods, importance sampling and weighted bootstrap assuming scale parameter as known. The estimates by non iterative techniques do not depend on the specification of hyper parameters which is optimal from the Bayesian point of view. The estimates obtained by more sophisticated Gibbs sampler vary slightly with the choices of hyper parameters. The objective of this paper is to illustrate these tools in a simpler setup which may be essential in more complicated situations.

• Journal of the Korean Data and Information Science Society
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• v.16 no.3
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• pp.629-638
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• 2005

We derive the approximate maximum likelihood estimators of the scale parameter and location parameter of the extreme value distribution based on multiply Type-II censored samples. We compare the proposed estimators in the sense of the mean squared error for various censored samples.

• Communications for Statistical Applications and Methods
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• v.26 no.2
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• pp.91-102
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• 2019

In this paper, we propose a new estimation method based on a weighted linear regression framework to obtain some estimators for unknown parameters in a two-parameter Rayleigh distribution under a progressive Type-II censoring scheme. We also provide unbiased estimators of the location parameter and scale parameter which have a nuisance parameter, and an estimator based on a pivotal quantity which does not depend on the other parameter. The proposed weighted least square estimator (WLSE) of the location parameter is not dependent on the scale parameter. In addition, the WLSE of the scale parameter is not dependent on the location parameter. The results are compared with the maximum likelihood method and pivot-based estimation method. The assessments and comparisons are done using Monte Carlo simulations and real data analysis. The simulation results show that the estimators ${\hat{\mu}}_u({\hat{\theta}}_p)$ and ${\hat{\theta}}_p({\hat{\mu}}_u)$ are superior to the other estimators in terms of the mean squared error (MSE) and bias.

• The Journal of the Korea Contents Association
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• v.21 no.3
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• pp.616-625
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• 2021

Deep neural networks are an approximation method that approximates an arbitrary function to a linear model and then repeats additional approximation using a nonlinear active function. In this process, the method of evaluating the performance of approximation uses the loss function. Existing in-depth learning methods implement approximation that takes into account loss functions in the linear approximation process, but non-linear approximation phases that use active functions use non-linear transformation that is not related to reduction of loss functions of loss. This study proposes parametric activation functions that introduce scale parameters that can change the scale of activation functions and location parameters that can change the location of activation functions. By introducing parametric activation functions based on scale and location parameters, the performance of nonlinear approximation using activation functions can be improved. The scale and location parameters in each hidden layer can improve the performance of the deep neural network by determining parameters that minimize the loss function value through the learning process using the primary differential coefficient of the loss function for the parameters in the backpropagation. Through MNIST classification problems and XOR problems, parametric activation functions have been found to have superior performance over existing activation functions.