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 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 Estimation in the Pareto Distribution

1990 ◽  
Vol 20 (2) ◽  
pp. 201-216 ◽  
Author(s):  
Mette Rytgaard
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Risk Premium ◽  
Unbiased Estimator ◽  
Minimum Variance ◽  
Credibility Theory ◽  
Likelihood Estimator ◽  
Minimum Variance Unbiased Estimator ◽  
The Moment ◽  
Alternative Estimator

AbstractIn the present paper, different estimators of the Pareto parameter α will be proposed and compared to each others.First traditional estimators of α as the maximum likelihood estimator and the moment estimator will be deduced and their statistical properties will be analyzed. It is shown that the maximum likelihood estimator is biased but it can easily be modified to an minimum-variance unbiased estimator of a. But still the coefficient of variance of this estimator is very large.For similar portfolios containing same types of risks we will expect the estimated α-values to be at the same level. Therefore, credibility theory is used to obtain an alternative estimator of α which will be more stable and less sensitive to random fluctuations in the observed losses.Finally, an estimator of the risk premium for an unlimited excess of loss cover will be proposed. It is shown that this estimator is a minimum-variance unbiased estimator of the risk premium. This estimator of the risk premium will be compared to the more traditional methods of calculating the risk premium.

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.

scholarly journals Estimation a Stress-Strength Model for P (Yr:n1 < Xk:n2 ) Using the Lindley Distribution

2017 ◽  
Vol 40 (1) ◽  
pp. 105-121 ◽  
Author(s):  
Marwa Khalil
Keyword(s):  
Maximum Likelihood ◽  
Simulation Study ◽  
Real Data ◽  
Minimum Variance ◽  
Strength Model ◽  
Practical Application ◽  
Likelihood Estimator ◽  
Lindley Distribution ◽  
Minimum Variance Unbiased Estimator ◽  
Proposed Model

The problem of estimation reliability in a multicomponent stress-strength model, when the system consists of k components have strength each compo- nent experiencing a random stress, is considered in this paper. The reliability of such a system is obtained when strength and stress variables are given by Lindley distribution. The system is regarded as alive only if at least r out of k (r < k) strength exceeds the stress. The multicomponent reliability of the system is given by Rr,k . The maximum likelihood estimator (M LE), uniformly minimum variance unbiased estimator (UMVUE) and Bayes esti- mator of Rr,k are obtained. A simulation study is performed to compare the different estimators of Rr,k . Real data is used as a practical application of the proposed model.

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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