• Communications for Statistical Applications and Methods
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• v.27 no.1
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• pp.47-64
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• 2020

In this paper, we derive some estimators of the scale parameter of the exponentiated half-logistic distribution based on the multiply Type-I hybrid censoring scheme. We assume that the shape parameter λ is known. We obtain the maximum likelihood estimator of the scale parameter σ. The scale parameter is estimated by approximating the given likelihood function using two different Taylor series expansions since the likelihood equation is not explicitly solved. We also obtain Bayes estimators using prior distribution. To obtain the Bayes estimators, we use the squared error loss function and general entropy loss function (shape parameter q = -0.5, 1.0). We also derive interval estimation such as the asymptotic confidence interval, the credible interval, and the highest posterior density interval. Finally, we compare the proposed estimators in the sense of the mean squared error through Monte Carlo simulation. The average length of 95% intervals and the corresponding coverage probability are also obtained.

• 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.

• Communications for Statistical Applications and Methods
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• v.21 no.6
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• pp.529-538
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• 2014

In this paper, we consider maximum likelihood estimators of normal distribution based on type II censoring. Gupta (1952) and Cohen (1959, 1961) required a table for an auxiliary function to compute since they did not have an explicit form; however, we derive an explicit form for the estimators using a method to approximate the likelihood function. The derived estimators are a special case of Balakrishnan et al. (2003). We compare the estimators with the Gupta's linear estimators through simulation. Gupta's linear estimators are unbiased and easily calculated; subsequently, the proposed estimators have better performance for mean squared errors and variances, although they show bigger biases especially when the ratio of the complete data is small.

• Journal of Korean Society for Quality Management
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• v.15 no.1
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• pp.20-32
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• 1987

Estimation for the parameters of a bivariate exponential (BVE) model of Marshall and Olkin (1967) is investigated for the cases of complete sampling and time-truncated parallel sampling. Maximum likelihood estimators, method of moment estimators and Bayes estimators for the parameters of a BVE model are obtained and compared with each other. A Monte Cario simulation study for a moderate sized samples indicates that the Bayes estimators of parameters perform better than their maximum likelihood and method of moment estimators.

• The Korean Journal of Applied Statistics
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• v.6 no.2
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• pp.393-399
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• 1993

When we compute the maximum likelihood estimators of the parameters for the logistic regression models, which are useful in studying the relationship between the binary response variable and the explanatory variable, the standard error calculations are usually based on the second derivative of log-likelihood function. On the other hand, an estimator of the Fisher information motivated from the fact that the expectation of the cross-product of the first derivative of the log-likelihood function gives the Fisher information is expected to have similar asymptotic properties. These estimators of Fisher information are closely related with the iterative algorithm to get the maximum likelihood estimator. The average numbers of iterations to achieve the maximum likelihood estimator are compared to find out which method is more efficient, and the estimators of the variance from each method are compared as estimators of the asymptotic variance.

• International Journal of Reliability and Applications
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• v.6 no.1
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• pp.41-51
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• 2005

The Bayes estimators of the parameters included in the complementary Weibull reliability model are obtained. In the process of deriving Bayes estimators, the scale and shape parameters of the complementary Weibull distribution are considered to be independent random variables having prior exponential distributions. The maximum likelihood estimators of the desired parameters are derived. Further, the least square estimators are obtained in closed forms. Simulation study is made using Monte Carlo method to make a comparison among the obtained estimators. The comparison is made by computing the root mean squared errors associated to each point estimation. Based on the numerical study, the Bayes procedure seems better than the maximum likelihood and least square procedures in the sense of having smaller root mean squared errors.

• 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.

• Communications for Statistical Applications and Methods
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• v.23 no.6
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• pp.479-496
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• 2016

In this survey, we present a modified inverse moment estimation of parameters and its applications. We use a specific model to demonstrate its principle and how to apply this method in practice. The estimation of unknown parameters is considered. A necessary and sufficient condition for the existence and uniqueness of maximum-likelihood estimates of the parameters is obtained for the classical maximum likelihood estimation. Inverse moment and modified inverse moment estimators are proposed and their properties are studied. Monte Carlo simulations are conducted to compare the performances of these estimators. As far as the biases and mean squared errors are concerned, modified inverse moment estimator works the best in all cases considered for estimating the unknown parameters. Its performance is followed by inverse moment estimator and maximum likelihood estimator, especially for small sample sizes.

• Communications for Statistical Applications and Methods
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• v.15 no.5
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• pp.765-774
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• 2008

In this paper, we derive the approximate maximum likelihood estimators(AMLEs) and maximum likelihood estimator of the scale parameter in a triangular distribution based on progressive Type-II censored samples. We compare the proposed estimators in the sense of the mean squared error through Monte Carlo simulation for various progressive censoring schemes.

• Water Engineering Research
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• v.4 no.3
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• pp.155-173
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• 2003

Parameters and quantiles of the 2-parameter generalized Pareto distribution were estimated using the methods of regular moments, modified moments, probability weighted moments, linear moments, maximum likelihood, and entropy for Monte Carlo-generated samples. The performance of these seven estimators was statistically compared, with the objective of identifying the most robust estimator. It was found that in general the methods of probability-weighted moments and L-moments performed better than the methods of maximum likelihood estimation, moments and entropy, especially for smaller values of the coefficient of variation and probability of exceedance.