• The Transactions of the Korea Information Processing Society
• /
• v.1 no.1
• /
• pp.14-22
• /
• 1994

This paper proposes two Bayes estimators and their evaluation algorithms of the software reliability at the end testing stage in the Smith's Bayesian software reliability growth model under the data prior distribution BE(a, b), which is more general than uniform distribution, as a class of prior information. We consider both a squared-error loss function and the Harris loss function in the Bayesian estimation procedures. We also compare the MSE performances of the Bayes estimators and their algorithms of software reliability using computer simulations. And we conclude that the Bayes estimator of software reliability under the Harris loss function is more efficient than other estimators in terms of the MSE performances as a is larger and b is smaller, and that the Bayes estimators using the beta prior distribution as a conjugate prior is better than the Bayes estimators under the uniform prior distribution as a noninformative prior when a＞b.

• Journal of the Korean Data and Information Science Society
• /
• v.18 no.1
• /
• pp.247-257
• /
• 2007

In this paper, we develop the noninformative priors for the common shape parameter in the gamma distributions. We develop the matching priors and reveal that the second order matching prior does not exist. It turns out that the one-at-a-time reference prior and the two group reference prior satisfy a first order probability matching criterion. Some simulation study is peformed.

• Journal of the Korean Statistical Society
• /
• v.35 no.3
• /
• pp.225-238
• /
• 2006

This paper considers noninformative priors for the scale parameter of exponential distribution when the data are collected in step stress accelerated life tests. We find the Jeffreys' and reference priors for this model and show that the reference prior satisfies first order matching criterion. Also, we show that there exists no second order matching prior in this problem. Some simulation results are given and we perform Bayesian analysis for proposed priors using some data.

• International Journal of Reliability and Applications
• /
• v.2 no.2
• /
• pp.117-130
• /
• 2001

Consider the problem of estimating the system reliability using noninformative priors when both stress and strength follow generalized gamma distributions. We first treat the orthogonal reparametrization and then, using this reparametrization, derive Jeffreys'prior, reference prior, and matching priors. We next provide the suffcient condition for propriety of posterior distributions under those noninformative priors. Finally, we provide and compare estimated values of the system reliability based on the simulated values of the parameter of interest in some special cases.

• Communications for Statistical Applications and Methods
• /
• v.18 no.4
• /
• pp.467-475
• /
• 2011

This paper develops the noninformative priors for the stress-strength reliability from one parameter generalized exponential distributions. When this reliability is a parameter of interest, we develop the first, second order matching priors, reference priors in its order of importance in parameters and Jeffreys' prior. We reveal that these probability matching priors are not the alternative coverage probability matching prior or a highest posterior density matching prior, a cumulative distribution function matching prior. In addition, we reveal that the one-at-a-time reference prior and Jeffreys' prior are actually a second order matching prior. We show that the proposed reference prior matches the target coverage probabilities in a frequentist sense through a simulation study and a provided example.

• Communications for Statistical Applications and Methods
• /
• v.14 no.1
• /
• pp.81-92
• /
• 2007

This paper consider trinomial group testing concerned with classification of N given units into one of k disjoint categories. In this paper, we propose Bayesian inference for estimating individual category proportions using the trinomial group testing model proposed by Bar-Lev et al. (2005). We compared a relative efficience (RE) based on the mean squared error (MSE) of MLE and Bayes estimators with various prior information. The impact of different prior specifications on the estimates is also investigated using selected prior distribution. The impact of different priors on the Bayes estimates is modest when the sample size and group size we large.

• Journal of the Korean Data and Information Science Society
• /
• v.13 no.2
• /
• pp.195-200
• /
• 2002

We consider the Bernoulli two-armed bandit problem. It is well known that the my optic strategy is optimal when the prior distribution is concentrated at two points in the unit square. We investigate several cases in the unit square whether the my optic strategy is optimal or not. In general, the my optic strategy is not optimal when the prior distribution is not concentrated at two points in the unit square.

• Journal of the Korean Data and Information Science Society
• /
• v.27 no.4
• /
• pp.1091-1100
• /
• 2016

This paper considers the noninformative priors for the linear function of parameters in the lognormal distribution. The lognormal distribution is applied in the various areas, such as occupational health research, environmental science, monetary units, etc. The linear function of parameters in the lognormal distribution includes the expectation, median and mode of the lognormal distribution. Thus we derive the probability matching priors and the reference priors for the linear function of parameters. Then we reveal that the derived reference priors do not satisfy a first order matching criterion. Under the general priors including the derived noninformative priors, we check the proper condition of the posterior distribution. Some numerical study under the developed priors is performed and real examples are illustrated.

• Journal of Integrative Natural Science
• /
• v.7 no.2
• /
• pp.138-144
• /
• 2014

Fisher information matrix plays an important role in statistical inference of unknown parameters. Especially, it is used in objective Bayesian inference where we calculate the posterior distribution using a noninformative prior distribution, and also in an example of metric functions in geometry. To estimate parameters in a distribution, we can use the Fisher information matrix. The more the number of parameters increases, the more its matrix form gets complicated. In this paper, by using Mathematica programs we derive the Fisher information matrix for 4-parameter generalized gamma distribution which is used in reliability theory.

• Journal of the Korean Data and Information Science Society
• /
• v.22 no.6
• /
• pp.1183-1197
• /
• 2011

The prior distribution is the probability distribution we have before observing data. Using Bayes' rule, we can compute the posterior distribution, the new probability distribution, after observing data. Computing the posterior distribution is much easier than before by using Excel VBA macro. In addition, we can conveniently compute the successive updating posterior distributions after observing the independent and sequential outcomes. In this paper we compose some Excel VBA macros for applying Bayes' rule and give some examples.