scholarly journals An Uniformly Minimum Variance Unbiased Point Estimator Using Fuzzy Observations

2016 ◽  
Vol 36 (4) ◽  
Author(s):  
Mohammad Ghasem Akbari ◽  
Abdolhamid Rezaei
Keyword(s):  
Random Sample ◽  
Unbiased Estimator ◽  
Probability Space ◽  
Minimum Variance ◽  
Point Estimation ◽  
New Method ◽  
Minimum Variance Unbiased Estimator ◽  
Fuzzy Point ◽  
Point Estimator ◽  
Fuzzy Random

This paper proposes a new method for uniformly minimum variance unbiased fuzzy point estimation. For this purpose we make use of a uniformly minimum variance unbiased estimator and we develop this new method for a fuzzy random sample ~X1,...,~Xn  is induced by  X1,,...,Xn  onthe same probability space.

scholarly journals Uniform Minimum Variance Unbiased Estimator of Fractal Dimension

2021 ◽  
Vol 9 (1) ◽  
pp. 63-68
Author(s):  
Zeny Maureal ◽  
◽  
Elmer Castillano ◽  
Roberto Padua ◽  
◽  
...  
Keyword(s):  
Unbiased Estimator ◽  
Random Variable ◽  
Minimum Variance ◽  
Statistical Characteristics ◽  
Fractional Dimension ◽  
Power Law Distribution ◽  
Likelihood Estimator ◽  
Minimum Variance Unbiased Estimator ◽  
Point Estimator ◽  
The Relationship

The paper introduced the concept of a fractal distribution using a power-law distribution. It proceeds to determining the relationship between fractal and exponential distribution using a logarithmic transformation of a fractal random variable which turns out to be exponentially distributed. It also considered finding the point estimator of fractional dimension and its statistical characteristics. It was shown that the maximum likelihood estimator of the fractional dimension λ is biased. Another estimator was found and shown to be a uniformly minimum variance unbiased estimator (UMVUE) by Lehmann-Scheffe’s theorem.

scholarly journals Active Control of Edgewise Vibrations in Wind Turbine Blades Using Stochastic Disturbance Accommodating Control

2017 ◽  
Author(s):  
Cong Cong
Keyword(s):  
Wind Turbine ◽  
Unbiased Estimator ◽  
Turbine Blades ◽  
Minimum Variance ◽  
Aerodynamic Load ◽  
Unknown Input ◽  
Linear Quadratic ◽  
Minimum Variance Unbiased Estimator ◽  
Stochastic Disturbance ◽  
Disturbance Accommodating Control

Vibrations of blades and tower have important impact for wind turbine. This paper presents a active controller design to suppress blade edgewise vibrations under aerodynamic load and gravitational load.Treating the sum of aerodynamic load input in edgewise direction and gravitational load as unknown disturbance input,a stochastic disturbance accommodating control(SDAC) approach is proposed to design a controller which it utilizes a minimum-variance unbiased estimator(MVUE) to estimate both state and unknown input. The stability analysis proved that the proposed SDAC is bounded in mean square.In order to verify the performance of the minimum-variance unbiased estimator and the proposed SDAC, numerical simulations using Matlab/Simulink have been carried out for the National Renewable Energy Laboratory 5-MW wind turbine.Under the different circumstance which exists the random process and measure noise and noise free. It is shown that the estimation value by MVUE can tracking the real state and unknown input. The results are also compared to the traditional linear quadratic regulator(LQR) and show that the proposed stochastic disturbance accommodating control scheme can further reduce displacement in edgewise vibrations direction and the control strategy is more effective than the LQR.

Determination of CRLB and Minimum Variance Unbiased Estimator of a DC Signal in AWGN Using Laplace Transform

2021 ◽  
Vol 40 (1) ◽  
pp. 79-86
Author(s):  
Abdi Abdalla
Keyword(s):  
Lower Bound ◽  
Gaussian Noise ◽  
Unbiased Estimator ◽  
Laplace Transformation ◽  
Additive White Gaussian Noise ◽  
Minimum Variance ◽  
Minimum Variance Unbiased Estimator ◽  
Mathematical Background ◽  
Alternative Approach

This paper presents an alternative approach for the determination of Cramer-Rao Lower Bound (CRLB) and Minimum Variance Unbiased Estimator (MVUE) using Laplace transformation. In this work, a DC signal in Additive White Gaussian Noise (AWGN) was considered. During the investigation, a number of experiments were conducted to analyze different possible outputs under different conditions, and then the patterns of the outcomes were studied. Finally closed-form expressions for the CRLB and MVUE were deduced employing the Laplace transformation. The resulting expressions show that the proposed method has almost the same number of steps as the existing method. However, the later requires only the knowledge of algebra to arrive at the CRLB expressions contrary to the existing approach where a strong mathematical background is required and hence making it superior over the existing method, in that sense.

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