Variances and covariances of the maximum entropy estimators for the Pearson type-3 distribution

1990 ◽  
Vol 17 (4) ◽  
pp. 590-596 ◽  
Author(s):  
Huynh Ngoc Phien ◽  
Van-Thanh-Van Nguyen
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Key Words ◽  
Maximum Entropy ◽  
Simulated Data ◽  
Distribution Method ◽  
Statistical Hydrology ◽  
Pearson Type ◽  
Type 3 ◽  
Parameter Estimators

Although the method of maximum entropy (MME) appears to be promising in fitting the Pearson type-3 distribution, the sampling properties of the estimators are not available. This paper provides the formulas needed for computing the variances and covariances of the parameter estimators and the variance of the T-year event. All needed formulas are derived analytically and related computation schemes are described. Through applications of the developed technique to actual and simulated data, it was found that the efficiency of the MME may be slightly improved when the biased sample variance is used instead of the unbiased one. Key words: Pearson type-3 distribution, method of maximum entropy, floods, statistical hydrology, Monte-Carlo simulation.

THERMODYNAMIC AND MAGNETIC PROPERTIES OF THE ARCHIMEDEAN LATTICES

2005 ◽  
Vol 19 (28) ◽  
pp. 4259-4267 ◽  
Author(s):  
Q. L. ZHANG
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Magnetic Properties ◽  
Free Energy ◽  
Thermodynamic Properties ◽  
Specific Heat ◽  
Internal Energy ◽  
Type 3 ◽  
Ising Spins ◽  
Frustration Effects

We numerically study the thermodynamic properties of two Archimedean lattices1 with Ising spins using Wang–Landau algorithm of the Monte Carlo simulation. The two Archimedean lattices are of the type (3, 122) and Kagomé, for which we are particularly interested in the frustration effects. The internal energy, specific heat, free energy, entropy, magnetization and spin susceptibility are calculated.

scholarly journals A GATE-based Monte Carlo simulation of a dual-layer pixelized gadolinium oxyorthosilicate (GSO) detector performance and response for micro PET scanner

1970 ◽  
Vol 47 (2) ◽  
pp. 507-519
Author(s):  
Leonid L Nkuba ◽  
Innocent J Lugendo ◽  
Idrissa S Amour
Keyword(s):  
Experimental Data ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Intensity Ratio ◽  
Simulated Data ◽  
Simulation Method ◽  
Detector Response ◽  
Simulation Platform ◽  
Detector Performance ◽  
Overlapping Bands

The purpose of this study was to simulate the GSO detector of a micro PET using GATE simulation platform. The performance and responses of the simulated GSO detector assembly were evaluated by comparing the simulated data to the experimental and XCOM data to validate the simulation platform and procedure. Based on NEMA NU-4 2008 protocols, the performance of GSO detector in terms of sensitivity was simulated and compared to the experimental data. Similarly, the GSO detector response to photons interaction was simulated and compared against the XCOM data for absorbed intensity ratio in the GSO detector and survived intensity ratio in Pb blocks. Results showed that simulated and experimental sensitivities agreed well with R2 of 0.995 and two overlapping bands at 95% confidence. An agreement with R2 of 0.972 and 0.973 as well as with overlapping bands at 95% confidence was obtained in simulated and XCOM data for absorbed and survived intensity ratio in the GSO detector and Pb blocks, respectively. The observed agreements demonstrate the accuracy of the simulation method to mimic the behaviour of the GSO detector. The validated GATE algorithm for micro PET scanner is therefore recommended for simulation and optimisation of collimator design in further studies. Keywords: GATE simulation, Experimental data, XCOM data, GSO detector, micro PET.  

scholarly journals An iterative method of statistical tolerancing based on the unified Jacobian–Torsor model and Monte Carlo simulation

2020 ◽  
Vol 7 (2) ◽  
pp. 165-176
Author(s):  
Heping Peng ◽  
Zhuoqun Peng
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Iterative Method ◽  
Iterative Process ◽  
Simulated Data ◽  
Small Displacement ◽  
Real Multiplication ◽  
Small Displacement Torsor ◽  
Statistical Tolerance

Abstract This paper focuses on exploring an iterative method of statistical tolerance design to guide designers to select tolerances more economically and effectively. After having identified the assembly functional requirement (FR) and the functional elements (FEs) of corresponding tolerance chain, the expression of a unified Jacobian–Torsor model can be derived. Monte Carlo simulation is employed to generate random variables simulating the variations of small displacement torsor associated with the FE pairs with all the generated random values being within the intervals constrained by the corresponding tolerance zones. Then, the real multiplication operations are repeatedly executed to this model, a large number of real torsor component values of FR will be obtained and we can perform statistical analysis for these simulated data to get the statistical limits of the assembly FR in the desired direction. The tolerances of critical FEs may need to be adjusted to satisfy the assembly FR imposed by the designer, and the percentage contribution of each FE to the assembly FR can help determine these critical tolerances that need to be tightened or loosened. Once the calculated FR is in close agreement with the imposed FR, the iterative process can be stopped, and the statistical tolerance redesign is achieved. The effectiveness of the proposed method is illustrated with a case study. Compared with the deterministic tolerancing method, the results show that the proposed method is more economical and that can relax significantly the precision required, manufacturing and inspection costs can then be reduced considerably.

scholarly journals Confidence Interval Estimation for Precipitation Quantiles Based on Principle of Maximum Entropy

Entropy ◽  
2019 ◽  
Vol 21 (3) ◽  
pp. 315 ◽  
Author(s):  
Ting Wei ◽  
Songbai Song
Keyword(s):  
Confidence Interval ◽  
Maximum Entropy ◽  
Confidence Intervals ◽  
Interval Estimation ◽  
Principle Of Maximum Entropy ◽  
Pearson Type ◽  
Confidence Interval Estimation ◽  
Type 3 ◽  
Methods Of Moments ◽  
Principle Of Maximum

The principle of maximum entropy (POME) has been used for a variety of applications in hydrology, however it has not been used in confidence interval estimation. Therefore, the POME was employed for confidence interval estimation for precipitation quantiles in this study. The gamma, Pearson type 3 (P3), and extreme value type 1 (EV1) distributions were used to fit the observation series. The asymptotic variances and confidence intervals of gamma, P3, and EV1 quantiles were then calculated based on POME. Monte Carlo simulation experiments were performed to evaluate the performance of the POME method and to compare with widely used methods of moments (MOM) and the maximum likelihood (ML) method. Finally, the confidence intervals T-year design precipitations were calculated using the POME for the three distributions and compared with those of MOM and ML. Results show that the POME is superior to MOM and ML in reducing the uncertainty of quantile estimators.

The Maximum Entropy Estimation of Structural Reliability Based on Monte Carlo Simulation

2014 ◽  
Author(s):  
Wenbo Huang ◽  
Jiangang Mao ◽  
Zhiyong Zhang
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Maximum Entropy ◽  
Failure Probability ◽  
Structural Reliability ◽  
High Efficiency ◽  
Numerical Examples ◽  
Entropy Estimation ◽  
Probabilistic Distribution ◽  
Maximum Entropy Estimation

Taking the advantage of the high efficiency of Monte Carlo simulation for events of high failure probability, it is adopted to estimate the probabilities of failure of the reduced safe margins of structures. By assuming that the low tail of the probabilistic distribution of the safe margin to follow a Weibull distribution, the failure probabilities simulated are taken as empirical data to extrapolate the Weibull parameters. Among the candidate Weibull distributions, the maximum entropy is used to identify the optimum one which is used to predict the truth probabilities of failure of structures. Two typical numerical examples are carried out to demonstrate the method developed.

Log Pearson Type 3 Distribution: Method of Mixed Moments

1980 ◽  
Vol 106 (6) ◽  
pp. 999-1019
Author(s):  
Donthamsetti Veerabhadra Rao
Keyword(s):  
Distribution Method ◽  
Pearson Type ◽  
Type 3
Sign in / Sign up

Export Citation Format

Share Document