This paper reviews statistical methods for analyzing output data from computer simulations. First, it focuses on the estimation of steady-state system parameters. The estimation techniques include the replication/deletion approach, the regenerative method, the batch means method, and methods based on standardized time series. Second, it reviews recent statistical procedures to find the best system among a set of competing alternatives.

Proceedings of the 2000 winter simulation conference

1. Models 1.1. Introduction 1.2. A Single-Server Queue 1.3. A Simple Inventory System 2. Random Number Generation 2.1. Lehmer Random Number Generation: Introduction 2.2. Lehmer Random Number Generation: Implementation 2.3. Monte Carlo Simulation 2.4. Monte Carlo Simulation Examples 3. Discrete-Event Simulation 3.1. Discrete-Event Simulation 3.2. Multi-Stream Lehmer Random Number Generation 3.3. Discrete-Event Simulation Models 4. Statistics 4.1. Sample Statistics 4.2. Discrete-Data Histograms 4.3. Continuous-Data Histograms 4.4. Correlation 5. Next-Event Simulation 5.1. Next-Event Simulation 5.2. Next-Event Simulation Examples 5.3. Event List Management 6. Discrete Random Variables 6.1. Discrete Random Variables 6.2. Generating Discrete Random Variables 6.3. Discrete Random Variable Applications 6.4. Discrete Random Variable Models 6.5. Random Sampling 7. Continuous Random Variables 7.1. Continuous Random Variables 7.2. Generating Continuous Random Variables 7.3. Continuous Random Variable Applications 7.4. Continuous Random Variable Models 7.5. Nonstationary Poisson Processes 7.6. Acceptance-Rejection 8. Input Modeling 8.1. Error in Discrete-Event Simulation 8.2. Modeling Stationary Processes 8.3. Modeling Nonstationary Processes 9. Output Analysis 9.1. Interval Estimation 9.2. Monte Carlo Estimation 9.3. Finite-Horizon and Infinite-Horizon Statistics 9.4. Batch Means 9.5. Steady-State Single-Server Service Node Statistics 10. Projects 10.1. Empirical Tests of Randomness 10.2. Birth-Death Processes 10.3. Finite-State Markov Chains 10.4. A Network of Single-Server Service Nodes Appendices: A. Simulation Languages B. Integer Arithmetic C. Parameter Estimation Summary D. Random Variate Models E. Random Variate Generators F. Correlation and Independence References

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Discrete-Event Simulation: A First Course

Rolling stock maintenance strategy selection, spares parts’ estimation, and replacements’ interval calculation

The study presents the analysis of wind speed data from seven stations in Saudi Arabia, measured at 20, 30, and 40 m height above ground level (AGL) over a period varying from 2 to 5 years. Specifically, Weibull parameters were calculated using five different methods, four of them based on the statistical analysis of the collected data and a fifth one based on WAsP algorithm used in WindoGrapher software. The calculated values using the five different methods were found to be in good agreement at all the measurement heights. The correlation between the monthly mean values of Weibull scale parameter and the measured wind speed values was found to be linear for all the sites. The linear coefficient ‘a’ was found to be site's characteristic value and independent of the height AGL for most of the locations. Moreover, linearity has been substantiated between the monthly mean wind power density (WPD) and the corresponding measured wind speed for all the stations, with linear coefficients ‘a’ directly proportion...

Weibull Parameters Estimation Using Four Different Methods and Most Energy-Carrying Wind Speed Analysis

In hydrological statistics, the traditional assessment of goodness of fit test is interested in the testing precision to the sample generated from supposed PDF. However, the ability to reject the hypotheses when the supposed PDF is different from real PDF should be also emphasized. In addition, the sensitivity of test method to series length is important in hydrological analysis. Three methods of goodness of fit test that include Chi-Square (C-S), Kolmogorov-Smirnov (K-S), and Anderson-Darling (A-D) tests are applied in this study. The results of power test indicate that the most powerful tests for normal, uniform, P3, and Weibull distribution are K-S, C-S, and A-D tests, respectively. The test method with the best comprehensive power is C-S test, followed by K-S and A-D test.

/pdf/evaluating-the-three-methods-of-goodness-of-fit-test-for-37kl86mubm.pdf

Evaluating the Three Methods of Goodness of Fit Test for Frequency Analysis

Estimation of the three parameter Weibull probability distribution

Parameter estimation of the Weibull probability distribution

Summary We develop a general statistical procedure to obtain linearly the best efficient estimate of existing estimations of the parameter of a probability process. This procedure is used to obtain the best efficient estimates of the shape parameter, the intensity failure function and its reciprocal of the power law process. These estimates are important in the study of reliability growth modelling. The effectiveness of our findings is illustrated analytically and numerically, using real data and numerical simulations.

Best efficient estimates of the intensity function of the power law process

Bimodal nonparametric density estimation

Power law process is an important model in reliability analysis of engineering systems experiencing reliability growth or decay. Existing articles mainly deal with the estimation of the shape parameter. The estimation of the scale parameter is either ignored or dealt with very inefficiently. In this article, we are going to explain why those methods can estimate the shape parameter well, but fail to estimate the scale parameter effectively. It is still open problem if we can obtain an estimate to the scale parameter as good as the one to the shape parameter. We try to explore a new way to improve the estimate of the scale parameter. which will be proven better than the existing methods in theory and practice.

Hongzhu Qiao

Papers

Estimation of the three parameter Weibull probability distribution

Parameter estimation of the Weibull probability distribution

Best efficient estimates of the intensity function of the power law process

Bimodal nonparametric density estimation

Parameter estimation of power law process