• The Korean Journal of Applied Statistics
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• v.19 no.2
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• pp.217-230
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• 2006

e discuss proper confidence intervals for interval estimation of a low binomial proportion. A large sample surveys are practically executed to find rates of rare diseases, specified industrial disaster, and parasitic infection. Under the conditions of 0 < p ${\leq}$ 0.1 and large n, we compared 6 confidence intervals with mean coverage probability, root mean square error and mean expected widths to search a good one for interval estimation of population proportion p. As a result of comparisons, Mid-p confidence interval is best and AC, score and Jeffreys confidence intervals are next.

• Structural Engineering and Mechanics
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• v.25 no.3
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• pp.331-345
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• 2007

Uncertainties enter a complex analysis from a variety of sources: variability, lack of data, human errors, model simplification and lack of understanding of the underlying physics. However, for many important engineering applications insufficient data are available to justify the choice of a particular probability density function (PDF). Sometimes the only data available are in the form of interval estimates which represent, often conflicting, expert opinion. In this paper we demonstrate that Bayesian estimation techniques can successfully be used in applications where only vague interval measurements are available. The proposed approach is intended to fit within a probabilistic framework, which is established and widely accepted. To circumvent the problem of selecting a specific PDF when only little or vague data are available, a hierarchical model of a continuous family of PDF's is used. The classical Bayesian estimation methods are expanded to make use of imprecise interval data. Each of the expert opinions (interval data) are interpreted as random interval samples of a parent PDF. Consequently, a partial conflict between experts is automatically accounted for through the likelihood function.

• Journal of Information Processing Systems
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• v.15 no.2
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• pp.331-343
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• 2019

Dynamic thermal rating of the overhead transmission lines is affected by many uncertain factors. The ambient temperature, wind speed and wind direction are the main sources of uncertainty. Measurement uncertainty is an important parameter to evaluate the reliability of measurement results. This paper presents the uncertainty analysis based on Monte Carlo. On the basis of establishing the mathematical model and setting the probability density function of the input parameter value, the probability density function of the output value is determined by probability distribution random sampling. Through the calculation and analysis of the transient thermal balance equation and the steady- state thermal balance equation, the steady-state current carrying capacity, the transient current carrying capacity, the standard uncertainty and the probability distribution of the minimum and maximum values of the conductor under 95% confidence interval are obtained. The simulation results indicate that Monte Carlo method can decrease the computational complexity, speed up the calculation, and increase the validity and reliability of the uncertainty evaluation.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.17 no.11
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• pp.2945-2965
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• 2023

The laser inertial measurement unit is a precision device widely used in rocket navigation system and other equipment, and its quality is directly related to navigation accuracy. In the quality evaluation of laser inertial measurement unit, there is inevitably uncertainty in the index input information. First, the input numerical information is in interval form. Second, the index input grade and the quality evaluation result grade are given according to different national standards. So, it is a key step to transform the interval information input by the index into the data form consistent with the evaluation result grade. In the case of uncertain input, this paper puts forward a method based on probability distribution to solve the problem of asymmetry between the reference grade given by the index and the evaluation result grade when evaluating the quality of laser inertial measurement unit. By mapping the numerical relationship between the designated reference level and the evaluation reference level of the index information under different distributions, the index evidence symmetrical with the evaluation reference level is given. After the uncertain input information is transformed into evidence of interval degree distribution by this method, the information fusion of interval degree distribution evidence is carried out by interval evidential reasoning algorithm, and the evaluation result is obtained by projection covariance matrix adaptive evolution strategy optimization. Taking a five-meter redundant laser inertial measurement unit as an example, the applicability and effectiveness of this method are verified.

• Proceedings of the IEEK Conference
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• 2003.07a
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• pp.169-173
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• 2003

In this paper, we analyze a time-based update method in location management and calculate the optimal time-interval. We obtain the probability that an MT is j rings away from the center cell. And using these values, an exact analysis is made for the time-based location management cost. From the result, when the time-based method is applied to location update, we can get the optimal time-interval which minimizes the location management cost.

• Communications for Statistical Applications and Methods
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• v.10 no.3
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• pp.779-793
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• 2003

In this paper, various methods for finding confidence intervals for common odds ratio $\psi$ of the K 2${\times}$2 tables are reviewed. Also we propose two jackknife confidence intervals and bootstrap confidence intervals for $\psi$. These confidence intervals are compared with the other existing confidence intervals by using Monte Carlo simulation with respect to the average coverage probability.

• Communications for Statistical Applications and Methods
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• v.7 no.3
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• pp.859-869
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• 2000

In this paper, various methods for finding confidence intervals for p of binomial parameter are reviewed. Also we introduce tow bootstrap confidence intervals for p. We compare the performance of bootstrap methods with other methods in terms of average coverage probability by Monte Carlo simulation. Advantages of these bootstrap methods are discussed.

• Communications for Statistical Applications and Methods
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• v.27 no.1
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• pp.47-64
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• 2020

In this paper, we derive some estimators of the scale parameter of the exponentiated half-logistic distribution based on the multiply Type-I hybrid censoring scheme. We assume that the shape parameter λ is known. We obtain the maximum likelihood estimator of the scale parameter σ. The scale parameter is estimated by approximating the given likelihood function using two different Taylor series expansions since the likelihood equation is not explicitly solved. We also obtain Bayes estimators using prior distribution. To obtain the Bayes estimators, we use the squared error loss function and general entropy loss function (shape parameter q = -0.5, 1.0). We also derive interval estimation such as the asymptotic confidence interval, the credible interval, and the highest posterior density interval. Finally, we compare the proposed estimators in the sense of the mean squared error through Monte Carlo simulation. The average length of 95% intervals and the corresponding coverage probability are also obtained.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.26 no.2
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• pp.1-8
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• 2003

The operation and management of a plant require proper accounting for the constraints coming from reliability requirements as well as from budget and resource considerations. Most of the mathematical methods to decide the inspection time interval for plant maintenance by reliability theory are too complicated to be solved. Moreover, the mathematical and theoretical models are not usually cases in the practical applications. In order to overcome these problems, we propose a new the decision-making method of optimal inspection interval to minimize the maintenance cost by reliability theory and genetic algorithm (GA). The most merit of the proposed method is to decide the inspection interval for a plant machine of which failure rate $\lambda$(t) conforms to any probability distribution. Therefore, this method is more practical. The efficiency of the proposed method is verified by comparing the results obtained by GA-based method with the inspection model haying regular time interval.

• Communications for Statistical Applications and Methods
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• v.9 no.2
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• pp.305-313
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• 2002

Regarding to inference about a scalar measure of internal scatter of Ρ-variate normal population, this paper considers an interval estimation of the generalized variance, │$\Sigma$│. Due to complicate sampling distribution, fully parametric frequentist approach for the interval estimation is not available and thus Bayesian method is pursued to calculate the highest probability density (HPD) interval for the generalized variance. It is seen that the marginal posterior distribution of the generalized variance is intractable, and hence a weighted Monte Carlo method, a variant of Chen and Shao (1999) method, is developed to calculate the HPD interval of the generalized variance. Necessary theories involved in the method and computation are provided. Finally, a simulation study is given to illustrate and examine the proposed method.