scholarly journals A Comparative Study of Traditional and Kullback-Leibler Divergence of Survival Functions Estimators for the Parameter of Lindley Distribution

2019 ◽  
Vol 48 (5) ◽  
pp. 45-53 ◽  
Author(s):  
Sultan Parveen ◽  
Sanjay Kumar Singh ◽  
Umesh Singh ◽  
Dinesh Kumar
Keyword(s):  
Maximum Likelihood ◽  
Comparative Study ◽  
Estimation Method ◽  
Point Estimation ◽  
Least Square ◽  
Simulation Studies ◽  
Survival Functions ◽  
Lindley Distribution ◽  
Leibler Divergence ◽  
Point Estimation Method

A new point estimation method based on Kullback-Leibler divergence of survival functions (KLS), measuring the distance between an empirical and prescribed survival functions, has been used to estimate the parameter of Lindley distribution. The simulation studies have been carried out to compare the performance of the proposed estimator with the corresponding Least square (LS), Maximum likelihood (ML) and Maximum product spacing (MPS) methods of estimation.

scholarly journals A New Extension of Quasi Lindley Distribution: Properties and Applications

2019 ◽  
Vol 7 (2) ◽  
pp. 28
Author(s):  
Patrick Udoudo Unyime ◽  
Ette Harrison Etuk
Keyword(s):  
Maximum Likelihood ◽  
Estimation Method ◽  
Quantile Function ◽  
Moment Generating Function ◽  
Point Estimation ◽  
Maximum Likelihood Estimates ◽  
Lindley Distribution ◽  
Likelihood Point ◽  
Point Estimation Method ◽  
New Distribution

In this paper, we introduced and studied the statistical properties of a new distribution called the Marshall-Olkin extended quasi Lindley distribution. Specifically, we derived the crude moment, moment generating function, quantile function, and distributions of order statisticsbased on the distribution. The maximum likelihood point estimation method was used to estimate the parameters of the newly introduced model. Some AR minfication processes were discussed. We illustrated the applicability of the distribution using a real dataset.Keywords: Marshal-Olkin family of distributions; maximum likelihood estimates; minification processes; quasi Lindley distribution; quantile function.

scholarly journals Allocation of EV Public Charging Station in Renewable based Distribution Network using HHO Considering Uncertainties and Traffic Congestion

2021 ◽  
Author(s):  
Arnab Pal ◽  
Aniruddha Bhattacharya ◽  
Ajoy Kumar Chakraborty
Keyword(s):  
Distribution System ◽  
Traffic Congestion ◽  
Distribution Network ◽  
Estimation Method ◽  
Point Estimation ◽  
Rank Test ◽  
Voltage Profile ◽  
Charging Station ◽  
Soft Computing Techniques ◽  
Point Estimation Method

Abstract Electric vehicle (EV) is the growing vehicular technology for sustainable development to reduce carbon emission and to save fossil fuel. The charging station (CS) is necessary at appropriate locations to facilitate the EV owners to charge their vehicle as well as to keep the distribution system parameters within permissible limits. Besides that, the selection of a charging station is also a significant task for the EV user to reduce battery energy wastage while reaching the EV charging station. This paper presents a realistic solution for the allocation of public fast-charging stations (PFCS) along with solar distributed generation (SDG). A 33 node radial distribution network is superimposed with the corresponding traffic network to allocate PFCSs and SDGs. Two interconnected stages of optimization are used in this work. The first part deals with the optimization of PFCS’s locations and SDG’s locations with sizes, to minimize the energy loss and to improve voltage profile using harris hawk optimization (HHO) and few other soft computing techniques. The second part handles the proper assignment of EVs to the PFCSs with less consumption of the EV’s energy considering the road distances with traffic congestion using linear programming (LP), where the shortest paths are decided by Dijkstra's algorithm. The 2m point estimation method (2m PEM) is employed to handle the uncertainties associated with EVs and SDGs. The robustness of solutions are tested using wilcoxon signed rank test and quade test.

scholarly journals Two-Stage Optimal Scheduling of Large-Scale Renewable Energy System Considering the Uncertainty of Generation and Load

2020 ◽  
Vol 10 (3) ◽  
pp. 971 ◽  
Author(s):  
Xiangyu Kong ◽  
Shuping Quan ◽  
Fangyuan Sun ◽  
Zhengguang Chen ◽  
Xingguo Wang ◽  
...  
Keyword(s):  
Renewable Energy ◽  
Demand Response ◽  
Large Scale ◽  
Thermal Power ◽  
Estimation Method ◽  
Point Estimation ◽  
Low Carbon ◽  
System Operation ◽  
Two Stage ◽  
Point Estimation Method

With the development of smart grid and low-carbon electricity, a high proportion of renewable energy is connected to the grid. In addition, the peak-valley difference of system load increases, which makes the traditional grid scheduling method no longer suitable. Therefore, this paper proposes a two-stage low-carbon economic scheduling model considering the characteristics of wind, light, thermal power units, and demand response at different time scales. This model not only concerns the deep peak state of thermal power units under the condition of large-scale renewable energy, but also sets the uncertain models of PDR (Price-based Demand Response) virtual units and IDR (Incentive Demand Response) virtual units. Taking the system operation cost and carbon treatment cost as the target, the improved bat algorithm and 2PM (Two-point Estimation Method) are used to solve the problem. The introduction of climbing costs and low load operating costs can more truly reflect the increased cost of thermal power units. Meanwhile, the source-load interaction can weigh renewable energy limited costs and the increased costs of balancing volatility. The proposed method can be applied to optimal dispatch and safe operation analysis of the power grid with a high proportion of renewable energy. Compared with traditional methods, the total scheduling cost of the system can be reduced, and the rights and obligations of contributors to system operation can be guaranteed to the greatest extent.

scholarly journals Calibration of MEMS Triaxial Accelerometers Based on the Maximum Likelihood Estimation Method

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Yifan Sun ◽  
Xiang Xu
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Random Noise ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Least Square ◽  
Triaxial Accelerometer ◽  
Zero Bias ◽  
Estimation Function ◽  
Maximum Likelihood Estimation Method

As a widely used inertial device, a MEMS triaxial accelerometer has zero-bias error, nonorthogonal error, and scale-factor error due to technical defects. Raw readings without calibration might seriously affect the accuracy of inertial navigation system. Therefore, it is necessary to conduct calibration processing before using a MEMS triaxial accelerometer. This paper presents a MEMS triaxial accelerometer calibration method based on the maximum likelihood estimation method. The error of the MEMS triaxial accelerometer comes into question, and the optimal estimation function is established. The calibration parameters are obtained by the Newton iteration method, which is more efficient and accurate. Compared with the least square method, which estimates the parameters of the suboptimal estimation function established under the condition of assuming that the mean of the random noise is zero, the parameters calibrated by the maximum likelihood estimation method are more accurate and stable. Moreover, the proposed method has low computation, which is more functional. Simulation and experimental results using the consumer low-cost MEMS triaxial accelerometer are presented to support the abovementioned superiorities of the maximum likelihood estimation method. The proposed method has the potential to be applied to other triaxial inertial sensors.

An IPEM for optimal control of uncertain beam-moving mass systems with saturation nonlinearity

2017 ◽  
Vol 24 (13) ◽  
pp. 2760-2781
Author(s):  
Xiao-Xiao Liu ◽  
Xing-Min Ren
Keyword(s):  
Nonlinear Control ◽  
Vibration Suppression ◽  
Estimation Method ◽  
Feedback System ◽  
Random Excitation ◽  
Point Estimation ◽  
Maximum Principles ◽  
Moving Mass ◽  
Nonlinear Feedback ◽  
Point Estimation Method

This paper addresses the vibration control of single-span beams subjected to a moving mass by coupling the saturated nonlinear control and an improved point estimation method (IPEM). An optimal nonlinear feedback control law, for a kind of uncertain linear system with actuator nonlinearities, is derived using the combination of Pontryagin's maximum principles and the improved point estimation method. The stability of the feedback system is guaranteed using a Lyapunov function. In order to obtain the instantaneously probabilistic information of output responses, a novel moment approach is presented by combining the improved point estimation method, the maximum entropy methodology and the probability density evolution theory. In addition to the consideration of stochastic system parameters, the external loadings are considered as a nonstationary random excitation and a moving sprung mass, respectively. The proposed strategy is then used to perform vibration suppression analysis and parametric sensitivity analysis of the given beam. From numerical simulation results, it is deduced that the improved point estimation method is a priority approach to the optimal saturated nonlinear control of stochastic beam systems. This observation has widespread applications and prospects in vehicle–bridge interaction and missile–gun systems.

Resonance Analysis of Train–Track–Bridge Interaction Systems with Correlated Uncertainties

2019 ◽  
Vol 20 (01) ◽  
pp. 2050008 ◽  
Author(s):  
Lifeng Xin ◽  
Xiaozhen Li ◽  
Jiaxin Zhang ◽  
Yan Zhu ◽  
Lin Xiao
Keyword(s):  
Probability Distributions ◽  
Three Dimensional ◽  
Estimation Method ◽  
Interaction Model ◽  
Point Estimation ◽  
Statistical Characteristics ◽  
Resonance Analysis ◽  
Track Bridge ◽  
Point Estimation Method ◽  
Nataf Transformation

Over the last decades, the resonance-related dynamics for bridge systems subjected to a moving train has been researched and discussed from mechanics, physics and mathematics. In the current work, new perspectives of train-induced resonance analysis are investigated through introducing random propagation process into the train–bridge dynamic interactions. Besides, the Nataf-transformation-based point estimation method is applied to generate pseudorandom variables following arbitrarily correlated probability distributions. A three-dimensional (3D) nonlinear train-ballasted track–bridge interaction model founded on fundamental physical and mechanical principles is employed to convey and depict train–bridge interactions with random properties considered. After that, extensive applications are illustrated in detail for revealing the statistical characteristics of the so-called “random resonance”. Numerical results show that the critical train speeds associated with resonance and cancelation are random in essence owing to the variability of system parameters; the correlation between parameters exerts obvious influences on system dynamic behaviors; the last vehicle of a train will be in more violent vibrations compared to the front vehicles; the influences of track irregularities on the wheel–rail interactions are significantly greater than those of resonance.

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