A Weighted Least-Squares Parametric Method of Reducing Nuclear-Reactor Gamma Spectral Data

1962 ◽  
pp. 306-323
Author(s):  
J. C. Whiton ◽  
R. L. Gamble ◽  
R. M. Thornton
Keyword(s):  
Least Squares ◽  
Spectral Data ◽  
Nuclear Reactor ◽  
Weighted Least Squares ◽  
Parametric Method

A Weighted Least-Squares Parametric Method of Reducing Nuclear-Reactor Gamma Spectral Data

1961 ◽  
Vol 5 ◽  
pp. 306-323
Author(s):  
J. C. Whiton ◽  
R. L. Gamble ◽  
R. M. Thornton
Keyword(s):  
Least Squares ◽  
Spectral Data ◽  
High Speed ◽  
Nuclear Reactor ◽  
Weighted Least Squares ◽  
Parametric Method ◽  
Pulse Height ◽  
Least Squares Fit ◽  
Pure Matrix ◽  
Program Error

AbstractA mathematical method has been developed which reduces nuclear-reactor gamma pulse-height spectral data to the form of differential energy spectra through the use of a high-speed computer machine. In essence, the method consists of a least-squares fit of weighted multichannel analyzer data and the utilization of curve-smoothing parametrization. The least-squares approach tends to reduce the magnitude of data that must be handled, i.e., reduces the order of matrix involved. Weighting is used to obtain fractional deviations for minimization by lease squares and thus obtain a satisfactory fit throughout the entire channel range. The parametrization smoothes the reduced data by making use of the fact that reactor gamma spectra can be represented by the product of an exponential and a polynomial. Difficulties that arise when pure matrix inversion is applied have been obviated, and the advantage of high-speed data reduction is gained through the use of an IBM 704-7090 computer program. Error analyses have been undertaken, and data have been reduced for comparative purposes. Results are included in the presentation of the investigation.

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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