Normal law of measurement error distribution

1962 ◽  
Vol 5 (4) ◽  
pp. 271-272
Author(s):  
G. S. Simkin
Keyword(s):  
Measurement Error ◽  
Error Distribution ◽  
Normal Law

Features of accumulation of amounts of measurement error

2017 ◽  
Vol 928 (10) ◽  
pp. 58-63 ◽  
Author(s):  
V.I. Salnikov
Keyword(s):  
Measurement Error ◽  
Confidence Interval ◽  
Normal Distribution ◽  
Confidence Level ◽  
Measurement Errors ◽  
Truncated Normal Distribution ◽  
Truncated Normal ◽  
The Law ◽  
Normal Law

The initial subject for study are consistent sums of the measurement errors. It is assumed that the latter are subject to the normal law, but with the limitation on the value of the marginal error Δpred = 2m. It is known that each amount ni corresponding to a confidence interval, which provides the value of the sum, is equal to zero. The paradox is that the probability of such an event is zero; therefore, it is impossible to determine the value ni of where the sum becomes zero. The article proposes to consider the event consisting in the fact that some amount of error will change value within 2m limits with a confidence level of 0,954. Within the group all the sums have a limit error. These tolerances are proposed to use for the discrepancies in geodesy instead of 2m*SQL(ni). The concept of “the law of the truncated normal distribution with Δpred = 2m” is suggested to be introduced.

Some sources of error and possible bias in Danscan ultrasonic measurements of cattle

1983 ◽  
Vol 37 (1) ◽  
pp. 67-71
Author(s):  
J. P. Gibson ◽  
J. C. Alliston
Keyword(s):  
Measurement Error ◽  
Mean Value ◽  
Time Of Day ◽  
Error Distribution ◽  
The Body ◽  
Residual Error ◽  
Ultrasonic Measurements ◽  
The Mean ◽  
Ultrasonic Images ◽  
Account Variation

ABSTRACTPhotographs of ultrasonic images of 10 animals were taken. Two replicate photographs were taken at each of four body positions (10th rib, 13th rib, 3rd lumbar and hindquarter) on both sides of the body in the morning and the afternoon of the day of scanning. Several measurements were taken on each photograph by an experienced interpreter. Replicate photographs failed to account for all possible sources of measurement error. Since neither time of day nor side of the body affected the mean value, taking observations at different times of the day or on both sides of the body could permit most sources of measurement error to be taken into account. Variation due to errors of measurement and differences among animals are presented. The residual error distribution contained several extreme outliers.It was concluded that a better understanding of all the sources of bias and error will be needed if ultrasonic measurements are to be more widely used.

scholarly journals Estimation in linear errors-in-variables models with unknown error distribution

Biometrika ◽  
2020 ◽  
Vol 107 (4) ◽  
pp. 841-856
Author(s):  
Linh H Nghiem ◽  
Michael C Byrd ◽  
Cornelis J Potgieter
Keyword(s):  
Parameter Estimation ◽  
Measurement Error ◽  
Method Of Moments ◽  
Phase Function ◽  
Generalized Method Of Moments ◽  
Error Distribution ◽  
Outcome Variable ◽  
Model Parameters ◽  
Errors In Variables ◽  
Error Distributions

Summary Parameter estimation in linear errors-in-variables models typically requires that the measurement error distribution be known or estimable from replicate data. A generalized method of moments approach can be used to estimate model parameters in the absence of knowledge of the error distributions, but it requires the existence of a large number of model moments. In this paper, parameter estimation based on the phase function, a normalized version of the characteristic function, is considered. This approach requires the model covariates to have asymmetric distributions, while the error distributions are symmetric. Parameters are estimated by minimizing a distance function between the empirical phase functions of the noisy covariates and the outcome variable. No knowledge of the measurement error distribution is needed to calculate this estimator. Both asymptotic and finite-sample properties of the estimator are studied. The connection between the phase function approach and method of moments is also discussed. The estimation of standard errors is considered and a modified bootstrap algorithm for fast computation is proposed. The newly proposed estimator is competitive with the generalized method of moments, despite making fewer model assumptions about the moment structure of the measurement error. Finally, the proposed method is applied to a real dataset containing measurements of air pollution levels.

Measurement error models with a general class of error distribution

Statistics ◽  
2009 ◽  
Vol 44 (2) ◽  
pp. 119-127 ◽  
Author(s):  
Alexandre Galvão Patriota ◽  
Heleno Bolfarine
Keyword(s):  
Measurement Error ◽  
General Class ◽  
Error Distribution ◽  
Error Models ◽  
Measurement Error Models

scholarly journals IMPACT OF THE CROSS-TRACK ERROR DISTRIBUTION LAW ON SAFE NAVIGATION IN NARROW WATERS

2020 ◽  
Vol 30 (1) ◽  
pp. 58-66
Author(s):  
I.I. Vorokhobin ◽  
◽  
◽  
◽  
Keyword(s):  
Normal Distribution ◽  
Error Distribution ◽  
Distribution Law ◽  
Track Error ◽  
Safe Navigation ◽  
The Cross ◽  
Normal Law ◽  
Vessel Motion ◽  
Cross Track ◽  
The Impact

The paper indicates that navigation in narrow waters requires navigators to use means of passage safety assessment prior to choosing a route. It is pointed out that a relevant factor when assessing the safe passage probability is the cross-track error distribution law, whose impact is the subject of the research. The article analyses recent developments and publications that have begun investigating this subject, and highlights previously unsolved parts of the general problem. The results revealed two equivalent approaches, as well as a navigational safety parameter, which are used to determine the probability of safe navigation in narrow waters on the chosen route. The need to develop advanced predictive vessel motion models is noted, while many researchers study the design of an information system for vessel motion simulation with complex dynamic models and an intelligence system for vessel motion prediction that imitates the learning process of an autonomous control unit created with the use of the artificial neural network. Methods for identification of vessel manoeuvring models are shown. Based on the analysis of vessel hydrodynamics, a nonlinear model frame of vessel manoeuvring is established. The available publications suggest using compound laws of the first and second types for describing random errors in navigation measurements as an alternative to the normal distribution law. The article examines the dependence of the safe narrow waters passage probability on the cross-track error distribution law. The normal law and compound laws of the first and second types are considered as the cross-track error distribution laws. A formula for estimating the safe passage probability in the manoeuvring area is given, and expressions for the distribution function of the normal law and compound laws of both types are obtained. To assess the impact of the cross-track error distribution law for the same route, the safe passage probability for the normal distribution law, as well as compound laws of the first and second types, was calculated. For the same route, the probability of safe passage was calculated with the use of onedimensional and two-dimensional density models. It is shown that the average relative difference between the estimated safe passage probability for both models is 0.3%, which confirms the validity of using a one-dimensional cross-track error distribution density.

Application of Uniform Measurement Error Distribution

2016 ◽  
Author(s):  
Alan Ghazarians ◽  
Subrata Sanyal ◽  
Dennis H. Jackson
Keyword(s):  
Measurement Error ◽  
Error Distribution ◽  
Uniform Measurement

INFLUENCE OF MEASUREMENT ERROR DISTRIBUTION THE ACCURACY RATES OF THE CONTROL

2020 ◽  
pp. 48-52
Author(s):  
S. B. Danilevich ◽  
V. V. Tretyak
Keyword(s):  
Measurement Error ◽  
Measurement Uncertainty ◽  
Uniform Distribution ◽  
Error Distribution ◽  
Reliability Indicators ◽  
The Monte Carlo Method ◽  
Accuracy Of Measurements ◽  
Accuracy Rates ◽  
Weakly Dependent

The influence of the type of distribution of measurement error and measurement uncertainty on the reliability of the multiparameter measurement testing is studied. Indicators of testing reliability include the probability of a control error of type 2 (P2), as well as the risk of the customer Rз and the risk of the manufacturer Rп. These control reliability indicators were calculated for different values of measurement uncertainty. The study was performed using the Monte Carlo method (imitation modelling). Three models of measurement error distribution were used: normal distribution, triangular (Simpson) distribution, uniform distribution. The results obtained allow us to establish the measurement uncertainty that provides the required risk of the customer (or another indicator of reliability). The following was established. For the symmetric law of error distribution, the highest estimates of the reliability indicators take place with a uniform distribution of the measurement error. The probability of P2 is weakly dependent on the number of controlled parameters and the type of distribution of the measurement error, but it significantly depends on the accuracy of measurements. The customer's risk depends significantly on both the number of controlled parameters and the accuracy of measurements during control.

scholarly journals The Construction Method of BeiDou Satellite Navigation Measurement Error System

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Jun Xie ◽  
Jian-jun Zhang ◽  
Gang Wang
Keyword(s):  
Measurement Error ◽  
Estimation Method ◽  
Satellite Navigation ◽  
Error Distribution ◽  
Distribution Model ◽  
Empirical Estimation ◽  
Satellite Navigation System ◽  
Error System ◽  
Error Index ◽  
The Relationship

Based on the measurement error of pseudorange in BeiDou satellite navigation system, this paper analyzes the measurement principle of the system. Aiming at the difficulties in the system measurement error index system, an overall construction method of measurement error system based on empirical estimation method and error distribution model is proposed. Based on the Analytic Hierarchy Process, the correlation analysis model of the measurement error index is constructed, the relationship between the indicators is analyzed, and the system measurement error index hierarchy is constructed. Based on the empirical estimation method and the error distribution model, the index values are decomposed and assigned based on the final service performance of the system, and a clear representation of the complex relationship of index matching is achieved. Finally, by analyzing the principle of the positioning function in the ground transportation control mode, taking the satellite clock error as an example, the model is decomposed layer by layer and the relevant indicator items are established. The relationship between index terms was studied, and the value of the indicators was quantified. Compared with the actual operating conditions of the current system, the correctness of the method was verified, which provided a basis for the demonstration of the index values of satellite navigation systems. Based on the empirical estimation method and error distribution model as a new type of calculation method, the index system established under a certain set of conditions is reasonable, and it can be applied to the error control adjustment in satellite navigation system engineering construction.

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