• Communications for Statistical Applications and Methods
• /
• 제24권3호
• /
• 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
• /
• 제25권6호
• /
• 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
• /
• 제32권3호
• /
• 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
• /
• 제7권2호
• /
• 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
• /
• 제7권3호
• /
• 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
• /
• 제2권1호
• /
• 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
• /
• 제20권4호
• /
• 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.

• 응용통계연구
• /
• 제28권5호
• /
• pp.907-920
• /
• 2015

기하분포에 기초한 관리도는 불량품이 드물게 발생하는 고품질공정에서 불량률의 변화를 효율적으로 탐지할 수 있다고 알려져 있다. 이러한 관리도를 사용할 때 기본적인 가정은 관리상태일 때의 불량률이 알려져 있거나 또는 정확하게 추정되었다는 것이다. 그러나 고품질공정에서 불량률은 아주 작기 때문에 이를 정확하게 추정하기가 쉽지 않으며 또한 아주 큰 표본크기가 필요한 경우도 종종 발생한다. 일반적으로 제1국면에서 관리상태의 불량률을 추정할 때 최대우도추정량을 사용하지만, 이 논문에서는 베이즈추정량의 사용을 제안하였다. 베이즈추정량을 사용할 경우 실무자의 사전지식을 반영할 수 있으며 표본에 불량품이 발견되지 않을 경우 발생하는 최대우도추정량의 문제점을 해결할 수 있다는 장점이 있다. 기하 관리도와 기하누적합 관리도에서 베이즈추정량을 사용한 경우와 최대우도추정량을 사용한 경우를 비교한 결과, 표본의 크기가 크지 않은 경우 베이즈추정량을 사용하는 것의 효율이 더 좋음을 알 수 있었다.

• Journal of the Korean Statistical Society
• /
• 제28권1호
• /
• 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.

• 응용통계연구
• /
• 제15권1호
• /
• pp.119-128
• /
• 2002

Rao와 Yu(1994)는 소지역 추정(small area estimation) 문제를 해결하기 위한 방법으로 추정 시점과 인접지역 정보 등 보조정보와 과걱의 표본조사 결과를 모두 이용하는 모형과 그 모형으로 부터 경험적최량선형비편향추정량(Empirical Best Unbiased Predictor)을 제안하였다. 본 논문에서는 Rao와 Yu의 모형에서 미지의 모수에 대한 사전확률분포를 가정한 계층적 베이즈 추정량을 제안하고, 이를 미국의 주별 4인가족 소득추정문제에 적용하여 그 효율을 미국의 Census Bureau에서 사용하고 있는 경험적 베이즈추정량 및 이전에 제안된 다른 추정량들과 비교하였다.