• Journal of the Korean Data and Information Science Society
• /
• 제17권2호
• /
• pp.493-498
• /
• 2006

We shall consider the UMVUE of [P(Y>X)]$^k$ in a two parameter exponential distribution.

• Journal of the Korean Data and Information Science Society
• /
• 제12권2호
• /
• pp.65-69
• /
• 2001

MLE and UMVUE of the right-tail probability in a Levy distribution will be considered, and hence the UMVUE is more efficient in a sense of simulated MSE than the MLE of the right-tail probability.

• Journal of the Korean Data and Information Science Society
• /
• 제17권4호
• /
• pp.1405-1412
• /
• 2006

We shall derive the UMVUE of the tail probability in Poisson, Binomial, and negative Binomial distributions, and compare means squared errors of the UMVUE and the MLE of the tail probability in each case.

• Journal of the Korean Data and Information Science Society
• /
• 제18권1호
• /
• pp.259-267
• /
• 2007

We consider parametric estimation in a half-normal variable and a UMVUE of its right-tail probability. Also we consider estimation of reliability in two independent half-normal variables, and derive k-th moment of ratio of two same variables.

• Communications for Statistical Applications and Methods
• /
• 제8권1호
• /
• pp.249-256
• /
• 2001

We shall derive the MLE and UMVUE of Lorenz Curve and Gini Index in a Pareto distribution with the pdf(1.1) and their variances. And compare mean square errors(MSE) of the MLE and UMVUE of the Lorenz Curve and Gini Index in a Pareto distribution with pdf(1.1).

• Journal of the Korean Statistical Society
• /
• 제24권1호
• /
• pp.45-64
• /
• 1995

When a random sample is taken from a certain class of discrete and continuous distributions whose support depend on two parameters, we could find that there exists the complete and sufficient statistic for parameters which belong to a certain class, and fomulate the uniformly minimum variance unbiased estimator (UMVUE) of any estimable function. Some UMVUE's of parametric functions are illustrated for the class of the distribution. Especially, we find that the UMVUE of some estimable parametric function from the truncated normal distribution could be expressed by the version of the Mill's ratio.

• Journal of the Korean Data and Information Science Society
• /
• 제1권
• /
• pp.67-76
• /
• 1990

For a two-parameter Pareto distribution, the uniformly minimum variance unbiased estimateors(UMVUE) for the function of the two parameters are expressed in terms of confluent hypergeometric function. The variance of the UMVUE is also expressed in terms of hypergeometric function of several variables. UMVUE's for the ${\gamma}th$ moment about zero and several useful parametric functions, and their variances are obtained as special cases. The estimators of Baxter(1980) and Saksena and Johnson(1984) are special cases of our estimator.

• Journal of the Korean Data and Information Science Society
• /
• 제11권2호
• /
• pp.319-325
• /
• 2000

In this paper, we shall derive MLE's, modified MLE, MRE and UMVUE's of the shape and scale parameters in a generalized uniform distribution, and propose several estimators for the right-tail probability in a generalized uniform distribution using the proposed estimators for the shape and scale parameters. And we shall compare exactly MSE of the proposed estimators for the shape and the scale parameters, and compare numerically efficiencies for the several proposed estimators of the right-tail probability in a generalized uniform distribution by Monte Caslo methods.

• Journal of the Korean Data and Information Science Society
• /
• 제10권1호
• /
• pp.11-18
• /
• 1999

To estimate the mean and the variance of a lognormal distribution, Finney (1941) derived the uniformly minimun variance unbiased estimators(UMVUE) in the form of infinite series. However, the conditions ${\sigma}^{2}\;>\;n\;and\;{\sigma}^{2}\;<\;\frac{n}{4}$ for computing $E(\hat{\theta}_{AM})\;and\;E(\hat{\eta}^{2}_{AM})$ are necessary. In this paper, we give an alternative derivation of the UMVUE's.

• Journal of the Korean Data and Information Science Society
• /
• 제22권4호
• /
• pp.811-817
• /
• 2011

We shall introduce a general probability mass function which includes several discrete probability mass functions. Especially, when the random variable X is Poisson, binomial, and negative binomial random variables as some special cases of the introduced distribution, the maximum likelihood estimator (MLE) and the uniformly minimum variance unbiased estimator (UMVUE) of the probability P(X ${\leq}$ t) are considered. And the efficiencies of the MLE and the UMVUE of the reliability ar compared each other.