• Journal of the Korean Statistical Society
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• v.20 no.1
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• pp.57-66
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• 1991

This paper deals with the problem of estimating an arbitrary piecewise continuous function of the parameter under squared error loss in the one parameter exponential family. Using Blyth's(1951) method sufficient conditions are given for the admissibility of (possibly generalized Bayes) estimators. Also, some examples are provided for normal, binomial, and gamma distributions.

• Journal of the Korean Statistical Society
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• v.25 no.4
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• pp.577-588
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• 1996

The Bayes factor provides a possible hierarchical Bayesian approach for studying the change point problems. A hypothesis for testing change versus no change is considered using predictive distributions. When the underlying distribution is in one-parameter exponential family with conjugate priors, Bayes factors are investigated to the hypothesis above. Finally one example is provided .

• Communications for Statistical Applications and Methods
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• v.5 no.2
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• pp.539-557
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• 1998

This article is concerned with the problem of estimating the mean of a one-parameter exponential family through sequential sampling in three stages under quadratic error loss. This more general framework differs from those considered by Hall (1981) and others. The differences are : (i) the estimator and the final stage sample size are dependent; and (ii) second order approximation of a continuously differentiable function of the final stage sample size permits evaluation of the asymptotic regret through higher order moments. In particular, the asymptotic regret can be expressed as a function of both the skewness $\rho$ and the kurtosis $\beta$ of the underlying distribution. The conditions on $\rho$ and $\beta$ for which negative regret is expected are discussed. Further results concerning the stopping variable N are also presented. We also supplement our theoretical findings wish simulation results to provide a feel for the triple sampling procedure presented in this study.

• Communications for Statistical Applications and Methods
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• v.31 no.4
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• pp.427-440
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• 2024

The problem addressed is that of sequentially estimating the difference between the means of two populations with respect to the squared error loss, where each population distribution is a member of the one-parameter exponential family. A Bayesian approach is adopted in which the population means are estimated by the posterior means at each stage of the sampling process and the prior distributions are not specified but have twice continuously differentiable density functions. The main result determines an asymptotic second-order lower bound, as t → ∞, for the Bayes risk of a sequential procedure that takes M observations from the first population and t - M from the second population, where M is determined according to a sequential design, and t denotes the total number of observations sampled from both populations.

• Journal of the Korean Statistical Society
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• v.10
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• pp.128-139
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• 1981

The Bayesian sequential estimation problem for k parameters exponential families is considered using loss related to the Fisher information. Tractable expressions for the Bayes estimator and the posterior expected loss are found, and the myopic or one-step-ahead stopping rule is defined. Sufficient conditions are given for optimality of the myopic procedure, and the myopic procedure is shown to be asymptotically optimal in all cases considered.

• The Korean Journal of Applied Statistics
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• v.10 no.1
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• pp.105-119
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• 1997

Barnwal and Paul(1988) derived the likelihood ratio statistic and $C(\alpha)$ statistic for testing the equality of the means of several groups of count data in the presence of a common dispersion parameter. These tests are generalized to be applicable without the restriction of a common dispersion parameter. And the assumed model of data is also extended from negative binomial to double exponential Poisson model. Monte Carlo simulations show the superiority of $C(\alpha)$ statistic based on the double exponential Poisson family which has a very simple form and requires estimates of the parameters only under the null hypothesis.

• Bulletin of the Korean Mathematical Society
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• v.44 no.3
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• pp.419-428
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• 2007

The space of periodic Boehmians with $\Delta$-convergence is a complete topological algebra which is not locally convex. A family of Boehmians $\{T_\lambda\}$ such that $T_0$ is the identity and $T_{\lambda_1+\lambda_2}=T_\lambda_1*T_\lambda_2$ for all real numbers $\lambda_1$ and $\lambda_2$ is called a one-parameter group of Boehmians. We show that if $\{T_\lambda\}$ is strongly continuous at zero, then $\{T_\lambda\}$ has an exponential representation. We also obtain some results concerning the infinitesimal generator for $\{T_\lambda\}$.

• Asian Pacific Journal of Cancer Prevention
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• v.13 no.5
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• pp.1829-1831
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• 2012

Background: The generalized gamma distribution statistics constitute an extensive family that contains nearly all of the most commonly used distributions including the exponential, Weibull and log normal. A saturated version of the model allows covariates having effects through all the parameters of survival time distribution. Accelerated failure-time models assume that only one parameter of the distribution depends on the covariates. Methods: We fitted both the conventional GG model and the saturated form for each of its members including the Weibull and lognormal distribution; and compared them using likelihood ratios. To compare the selected parameter distribution with log logistic distribution which is a famous distribution in survival analysis that is not included in generalized gamma family, we used the Akaike information criterion (AIC; r=l(b)-2p). All models were fitted using data for 369 women age 50 years or more, diagnosed with stage IV breast cancer in BC during 1990-1999 and followed to 2010. Results: In both conventional and saturated parametric models, the lognormal was the best candidate among the GG family members; also, the lognormal fitted better than log-logistic distribution. By the conventional GG model, the variables "surgery", "radiotherapy", "hormone therapy", "erposneg" and interaction between "hormone therapy" and "erposneg" are significant. In the AFT model, we estimated the relative time for these variables. By the saturated GG model, similar significant variables are selected. Estimating the relative times in different percentiles of extended model illustrate the pattern in which the relative survival time change during the time. Conclusions: The advantage of using the generalized gamma distribution is that it facilitates estimating a model with improved fit over the standard Weibull or lognormal distributions. Alternatively, the generalized F family of distributions might be considered, of which the generalized gamma distribution is a member and also includes the commonly used log-logistic distribution.