• Communications for Statistical Applications and Methods
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• v.19 no.5
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• pp.697-704
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• 2012

The maximum likelihood(ML) estimation of the scale parameters of an exponential distribution based on progressive Type II censored samples is given. The sample is multiply censored (some middle observations being censored); however, the ML method does not admit explicit solutions. In this paper, we propose multiply progressive Type II censoring. This paper presents the statistical inference on the scale parameter for the exponential distribution when samples are multiply progressive Type II censoring. The scale parameter is estimated by approximate ML methods that use two different Taylor series expansion types ($AMLE_I$, $AMLE_{II}$). We also obtain the maximum likelihood estimator(MLE) of the scale parameter under the proposed multiply progressive Type II censored samples. We compare the estimators in the sense of the mean square error(MSE). The simulation procedure is repeated 10,000 times for the sample size n = 20 and 40 and various censored schemes. The $AMLE_{II}$ is better than MLE and $AMLE_I$ in the sense of the MSE.

• Journal of the Korean Data and Information Science Society
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• v.24 no.6
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• pp.1455-1464
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• 2013

This paper develops maximum likelihood estimators (MLEs) of unknown parameters in an exponentiated half-logistic distribution based on a progressively type-II censored sample. We obtain approximate confidence intervals for the MLEs by using asymptotic variance and covariance matrices. Using importance sampling, we obtain Bayes estimators and corresponding credible intervals with the highest posterior density and Bayes predictive intervals for unknown parameters based on progressively type-II censored data from an exponentiated half logistic distribution. For illustration purposes, we examine the validity of the proposed estimation method by using real and simulated data.

• Communications for Statistical Applications and Methods
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• v.18 no.5
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• pp.657-666
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• 2011

In this paper, we derive the maximum likelihood estimator(MLE) and some approximate maximum likelihood estimators(AMLEs) of the scale parameter in an exponentiated half logistic distribution based on progressively Type-II censored samples. We compare the proposed estimators in the sense of the mean squared error(MSE) through a Monte Carlo simulation for various censoring schemes. We also obtain the AMLEs of the reliability function.

• 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.

• Journal of the Korean Mathematical Society
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• v.44 no.3
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• pp.525-539
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• 2007

Consider the regression model $Y_i=g(x_i)+e_i\;for\;i=1,\;2,\;{\ldots},\;n$, where: (1) $x_i$ are fixed design points, (2) $e_i$ are independent random errors with mean zero, (3) g($\cdot$) is unknown regression function defined on [0, 1]. Under $Y_i$ are censored randomly, we discuss the asymptotic normality of the weighted kernel estimators of g when the censored distribution function is known or unknown.

• 한국데이터정보과학회:학술대회논문집
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• 2006.04a
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• pp.279-293
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• 2006

In this paper, we derive the approximate maximum likelihood estimators of the scale parameter and location parameter of the exponential distribution based on multiply Type-II censored samples. Then three type tests, including the modified Clamor-von Mises test, the modified Watson test and the modified Kolmogorov-Smirnov test are developed for the exponential distribution based on multiply Type-II censored samples by using the proposed estimators. For each test, Monte Carlo techniques are used to generate critical values. The powers of these tests are investigated under several alternative distributions.

• Journal of the Korean Data and Information Science Society
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• v.14 no.4
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• pp.983-988
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• 2003

When the available sample is multiply Type-II censored, the maximum likelihood estimators of the location and the scale parameters of two-parameter exponential distribution do not admit explicitly. In this case, we propose some approximate maximum likelihood estimators by approximating the likelihood equations appropriately. We present an example to illustrate these estimation methods.

• Journal of the Korean Data and Information Science Society
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• v.21 no.2
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• pp.317-325
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• 2010

In this paper, we develop four modified empirical distribution function (EDF) type tests using approximate maximum likelihood estimators for the half-logistic distribution based on multiply Type-II censored samples. We also propose modified normalize sample Lorenz curve polt and new test statistics. We compare the above test statistics in the sense of the power for various censored samples. We present an example to illustrate this method.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.147-158
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• 2004

Sufficient conditions are given under which a generalized class of kernel-type estimators allows asymptotic approximation on the modulus of continuity. This generalized class includes sample distribution function, kernel-type estimator of density function, and an estimator that may apply to the censored case. In addition, an application is given to asymptotic normality of recursive density estimators of density function at an unknown point.

• Communications for Statistical Applications and Methods
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• v.28 no.2
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• pp.99-118
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• 2021

In this paper, we introduce an extended form of the inverse power Lomax model via Marshall-Olkin approach. We call it the Marshall-Olkin inverse power Lomax (MOIPL) distribution. The four- parameter MOIPL distribution is very flexible which contains some former and new models. Vital properties of the MOIPL distribution are affirmed. Maximum likelihood estimators and approximate confidence intervals are considered under Type I censored samples. Maximum likelihood estimates are evaluated according to simulation study. Bayesian estimators as well as Bayesian credible intervals under symmetric loss function are obtained via Markov chain Monte Carlo (MCMC) approach. Finally, the flexibility of the new model is analyzed by means of two real data sets. It is found that the MOIPL model provides closer fits than some other models based on the selected criteria.