Estimation of Parameters of Pert Distribution by Using Method of Moments

The method of moments has been widely used for estimating the parameters of a distribution. Usually lower order moments are wont to find the parameter estimates as they're known to possess less sampling variability. The method of moments may be a technique for estimating the parameters of a statistical model. It works by finding values of the parameters that end in a match between the sample moments and therefore the population moments (as implied by the model). the Method of moment Estimator is used to find out Estimates the parameters of PERT Distribution. We also compare equispaced and unequispaced Optimally Constructed Grouped data by the method of an Asymptotically Relative Efficiency. We also computed Average Estimate (AE), Variance (VAR), Standard Deviation (STD), Mean Absolute Deviation (MAD), Mean Square Error (MSE), Simulated Error (SE) and Relative Absolute Bias (RAB) for both the parameters under grouped sample supported 1000 simulations to assess the performance of the estimators. Keywords: Method of Moments, PERT Distribution, equispaced and unequipped Optimal Grouped sample

Distributed drive electric autonomous vehicle steering angle control based on active disturbance rejection control

Based on active disturbance rejection control technique and characteristics of electric power steering, a steering angle tracking controller is designed, which consists of an aligning moment estimator to deal with modeling error and nonlinearity of electric power steering. The aligning moment estimator is based on an extended state observer and takes steering system friction and differential drive steering torque, which is a unique phenomenon in a distributed drive electric vehicle, into consideration. According to the estimated aligning moment and tracking differentiator, the steering angle tracking controller is designed based on a nonlinear state feedback control and feedforward compensation control laws. Results of various simulations and experiments, including pivot steering, step input steering, and sinusoidal input steering, show that the proposed controller has good performance in tracking reference steering angle and is convenient to implement. With the aligning moment estimator, the proposed controller shows better results in comparative experiments than a conditional integral-based steering angle tracking controller.

Minimax Estimation of the Scale Parameter of Laplace Distribution under Modified Linear Exponential (MLINEX) Loss Function

The main objective of this paper is to find the minimax estimator of the scale parameter of Laplace distribution under MLINEX loss function by applying the theorem of Lehmann (1950). The estimator is then compared with classical estimator like moment estimator with respect to mean square errors (MSEs) through R- Code simulation. The result has shown that the minimax estimator under MLINEX loss function is better than moment estimator for all sample sizes. Finally, mean square errors of different estimators corresponding to sample size are presented graphically.

Adaptive Moment Estimator (Adam) Optimizer in ITK v3

This document describes an ITK class implementing an Adaptive Moment Estimator (Adam) optimizer algorithm within the Insight Toolkit ITK www.itk.org. Adam is an adaptive gradient descent optimizer, which independently adaptively estimates the gradient descent step for each parameter, at each iteration, based on stored past gradients. The optimizer stores exponentially decaying averages of past gradients to estimate first moment (the mean) and the second moment (the variance) of the gradients to formulate update rule for present iteration. The Adam optimizer compares favorably to other adaptive learning-method algorithms, converges faster, and is robust to saddle point. This paper is accompanied with the source code, input data, parameters and output data that the authors used for validating the algorithm described in this paper.

Simple and Yet Efficient Estimators for Markovian Multiserver Queues

Estimators for the parameters of the Markovian multiserver queues are presented, from samples that are the number of clients in the system at arbitrary points and their sojourn times. As estimation in queues is a recognizably difficult inferential problem, this study focuses on the estimators for the arrival rate, the service rate, and the ratio of these two rates, which is known as the traffic intensity. Simulations are performed to verify the quality of the estimations for sample sizes up to 400. This research also relates notable new insights, for example, that the maximum likelihood estimator for the traffic intensity is equivalent to its moment estimator. Some limitations of the results are presented along with a detailed numerical example and topics for future developments in this research area.