A Differentiated Registration Method for Complex Surfaces

2013 ◽  
Vol 457-458 ◽  
pp. 1635-1638
Author(s):  
Gao Shan Tan ◽  
Li Yan Zhang ◽  
Sheng Lan Liu ◽  
Qing Lan Shi
Keyword(s):  
Least Squares ◽  
Weighted Least Squares ◽  
Error Distribution ◽  
Great Flexibility ◽  
Precision Engineering ◽  
Registration Method ◽  
Weight Factors ◽  
Relationship Of ◽  
Inaccurate Result ◽  
Nominal Surface

Different error requirements on different surfaces are necessary in many situations. If the registration between the measured dataset and the nominal surface is performed ignoring these differences, an inaccurate result could occur due to the surfaces which have low precision. An improper registration even results in false verdict. So the differentiated registration is of significance in precision engineering. In this paper, a new registration method taking into consideration of the different error requirements is proposed. Firstly surfaces are classified based on different error requirement. Then, appropriate weight factors are iteratively given to these surfaces. Based on the change relationship of error and weight factors, the algorithm controls the error distribution by optimizing the weighted least squares. Our method has the great flexibility in distributing the error, which is suitable for engineering applications. The experiment demonstrates the validity.

Evaluation for estimating of the PDF and the CDF of Generalized Inverted Exponential Distribution with Application in Industry

2020 ◽  
pp. 507-522
Author(s):  
Parisa Torkaman
Keyword(s):  
Least Squares ◽  
Exponential Distribution ◽  
Mean Squared Error ◽  
Weighted Least Squares ◽  
Real Data ◽  
Minimum Variance ◽  
Cumulative Distribution ◽  
Estimation Methods ◽  
Data Set ◽  
Better Than

The generalized inverted exponential distribution is introduced as a lifetime model with good statistical properties. This paper, the estimation of the probability density function and the cumulative distribution function of with five different estimation methods: uniformly minimum variance unbiased(UMVU), maximum likelihood(ML), least squares(LS), weighted least squares (WLS) and percentile(PC) estimators are considered. The performance of these estimation procedures, based on the mean squared error (MSE) by numerical simulations are compared. Simulation studies express that the UMVU estimator performs better than others and when the sample size is large enough the ML and UMVU estimators are almost equivalent and efficient than LS, WLS and PC. Finally, the result using a real data set are analyzed.

scholarly journals Outlier Detection Algorithms Over Fuzzy Data with Weighted Least Squares

2021 ◽  
Author(s):  
Natalia Nikolova ◽  
Rosa M. Rodríguez ◽  
Mark Symes ◽  
Daniela Toneva ◽  
Krasimir Kolev ◽  
...  
Keyword(s):  
Least Squares ◽  
Outlier Detection ◽  
Weighted Least Squares ◽  
Fuzzy Data ◽  
Detection Algorithms

scholarly journals A New Inverted Topp-Leone Distribution: Applications to the COVID-19 Mortality Rate in Two Different Countries

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 25 ◽  
Author(s):  
Ehab Almetwally ◽  
Randa Alharbi ◽  
Dalia Alnagar ◽  
Eslam Hafez
Keyword(s):  
Statistical Model ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Likelihood Estimation ◽  
Linear Representation ◽  
Rate Function ◽  
Estimation Methods ◽  
Unknown Parameters ◽  
Least Squares Estimators ◽  
New Distribution

This paper aims to find a statistical model for the COVID-19 spread in the United Kingdom and Canada. We used an efficient and superior model for fitting the COVID 19 mortality rates in these countries by specifying an optimal statistical model. A new lifetime distribution with two-parameter is introduced by a combination of inverted Topp-Leone distribution and modified Kies family to produce the modified Kies inverted Topp-Leone (MKITL) distribution, which covers a lot of application that both the traditional inverted Topp-Leone and the modified Kies provide poor fitting for them. This new distribution has many valuable properties as simple linear representation, hazard rate function, and moment function. We made several methods of estimations as maximum likelihood estimation, least squares estimators, weighted least-squares estimators, maximum product spacing, Crame´r-von Mises estimators, and Anderson-Darling estimators methods are applied to estimate the unknown parameters of MKITL distribution. A numerical result of the Monte Carlo simulation is obtained to assess the use of estimation methods. also, we applied different data sets to the new distribution to assess its performance in modeling data.

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