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

• Journal of the Korean Data and Information Science Society
• /
• v.25 no.6
• /
• pp.1549-1555
• /
• 2014

Consider a p-variate normal distribution ($p-q{\geq}3$, q = rank($P_V$) with a projection matrix $P_V$). Using a simple property of noncentral chi square distribution, the generalized Bayes estimators dominating the James-Stein estimator shrinking towards projection vectors under quadratic loss are given based on the methods of Brown, Brewster and Zidek for estimating a normal variance. This result can be extended the cases where covariance matrix is completely unknown or ${\sum}={\sigma}^2I$ for an unknown scalar ${\sigma}^2$.

• Journal of the Korean Statistical Society
• /
• v.32 no.3
• /
• pp.261-270
• /
• 2003

This paper introduces a new density estimator which is Hellinger consistent under a simple condition. A number of issues are discussed, such as extension to Kullback-Leibler consistency, robustness, the Bayes version of the estimator and the maximum likelihood case. An illustration is presented.

• Communications for Statistical Applications and Methods
• /
• v.7 no.2
• /
• pp.525-531
• /
• 2000

Bayes estimators for reliability of a two-unit hot standby system with the imperfect switch based upon a complete sample of failure times observed from exponential distributions under squared error loss and some priors for failure rates are proposed, and mean squared errors of proposed several Bayes estimators for the system reliability are compared unmerically each other through the Monte Carlo simulation.

• Communications for Statistical Applications and Methods
• /
• v.7 no.3
• /
• pp.829-836
• /
• 2000

We shall derive Bayes estimators for he smaller and larger of two Pareto scale parameters with a common known shape parameter when the order of the scales is unknown and sample sizes are equal under squared error loss function. Also, we shall obtain biases and man squared errors for proposed Bayes estimators, and compare numerically performances for the proposed Bayes estimators.

• International Journal of Reliability and Applications
• /
• v.2 no.1
• /
• pp.49-56
• /
• 2001

In this paper we consider empirical Bayes estimation of the hazard rate and survival probabilities with right censored data under the assumption that the hazard function is constant over the period of observation and the prior distribution is gamma. We provide an estimator of the first derivative of the prior moment generating function that converges at each point to the true value in $L_2$ and use it to obtain, easy to compute, asymptotically optimal estimators under the squared error loss function.

• Communications for Statistical Applications and Methods
• /
• v.20 no.4
• /
• pp.321-327
• /
• 2013

Bayesian and empirical Bayesian methods have become quite popular in the theory and practice of statistics. However, the objective is to often produce an ensemble of parameter estimates as well as to produce the histogram of the estimates. For example, in insurance pricing, the accurate point estimates of risk for each group is necessary and also proper dispersion estimation should be considered. Well-known Bayes estimates (which is the posterior means under quadratic loss) are underdispersed as an estimate of the histogram of parameters. The adjustment of Bayes estimates to correct this problem is known as constrained Bayes estimators, which are matching the first two empirical moments. In this paper, we propose a way to apply the constrained Bayes estimators in insurance pricing, which is required to estimate accurately both location and dispersion. Also, the benefit of the constrained Bayes estimates will be discussed by analyzing real insurance accident data.

• The Korean Journal of Applied Statistics
• /
• v.28 no.5
• /
• pp.907-920
• /
• 2015

Charts based on geometric distribution are effective to monitor the proportion of nonconforming items in high-quality processes where the in-control proportion nonconforming is low. The implementation of this chart is often based on the assumption that in-control proportion nonconforming is known or accurately estimated. However, accurate parameter estimation is very difficult and may require a larger sample size than that available in practice for high-quality process where the proportion of nonconforming items is very small. An inaccurate estimate of the parameter can result in estimated control limits that cause unreliability in the monitoring process. The maximum likelihood estimator (MLE) is often used to estimate in-control proportion nonconforming. In this paper, we recommend a Bayes estimator for the in-control proportion nonconforming to incorporate practitioner knowledge and avoid estimation issues when no nonconforming items are observed in the Phase I sample. The effects of parameter estimation on the geometric chart and the geometric CUSUM chart are considered when the MLE and the Bayes estimator are used. The results show that chart performance with estimated control limits based on the Bayes estimator is generally better than that based on the MLE.

• Journal of the Korean Statistical Society
• /
• v.28 no.1
• /
• pp.93-106
• /
• 1999

In this paper we consider estimation of a real valued parameter in the drift coefficient of a Hilbert space valued Ito stochastic differential equation. First we consider observation of the corresponding diffusion in a fixed time interval [0, T] and prove the Bernstein - von Mises theorem concerning the convergence of posterior distribution of the parameter given the observation, suitably normalised and centered at the MLE, to the normal distribution as Tlongrightarrow$\infty$. As a consequence, the Bayes estimator of the drift parameter becomes asymptotically efficient and asymptotically equivalent to the MLE as Tlongrightarrow$\infty$. Next, we consider observation in a random time interval where the random time is determined by a predetermined level of precision. We show that the sequential MLE is better than the ordinary MLE in the sense that the former is unbiased, uniformly normally distributed and efficient but is latter is not so.

• The Korean Journal of Applied Statistics
• /
• v.15 no.1
• /
• pp.119-128
• /
• 2002

In this paper, we consider the HB estimators of small area means with repeated survey. mao and Yu(1994) considered small area model with repeated survey data and proposed empirical best linear unbiased estimators. We propose a hierachical Bayes version of Rao and Yu by assigning prior distributions for unknown hyperparameters. We illustrate our HB estimator using very popular data in small area problem and then compare the results with the estimator of Census Bureau and other estimators previously proposed.