Result: Parameter Estimation Through Weighted Least-Squares Rank Regression with Specific Reference to the Weibull and Gumbel Distributions
Title:
Parameter Estimation Through Weighted Least-Squares Rank Regression with Specific Reference to the Weibull and Gumbel Distributions
Authors:
Source:
Communications in statistics. Simulation and computation. 41(8-10):1654-1666
Publisher Information:
Colchester: Taylor & Francis, 2012.
Publication Year:
2012
Physical Description:
print, 3/4 p
Original Material:
INIST-CNRS
Subject Terms:
Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Probabilités et statistiques, Probability and statistics, Théorie des probabilités et processus stochastiques, Probability theory and stochastic processes, Lois de probabilités, Distribution theory, Statistiques, Statistics, Inférence non paramétrique, Nonparametric inference, Inférence linéaire, régression, Linear inference, regression, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Probabilités et statistiques numériques, Numerical methods in probability and statistics, Analyse covariance, Covariance analysis, Análisis covariancia, Analyse numérique, Numerical analysis, Análisis numérico, Analyse variance, Variance analysis, Análisis variancia, Distribution statistique, Statistical distribution, Distribución estadística, Estimation non paramétrique, Non parametric estimation, Estimación no paramétrica, Estimation paramètre, Parameter estimation, Estimación parámetro, Estimation statistique, Statistical estimation, Estimación estadística, Fonction répartition, Distribution function, Función distribución, Grand échantillon, Large sample, Loi Weibull, Weibull distribution, Ley Weibull, Loi probabilité, Probability distribution, Ley probabilidad, Méthode Monte Carlo, Monte Carlo method, Método Monte Carlo, Méthode moindre carré, Least squares method, Método cuadrado menor, Méthode statistique, Statistical method, Método estadístico, Méthode stochastique, Stochastic method, Método estocástico, Petit échantillon, Small sample, Pequeña muestra, Probabilité, Probability, Probabilidad, Régression statistique, Statistical regression, Regresión estadística, Simulation numérique, Numerical simulation, Simulación numérica, Statistique ordre, Order statistic, Estadística orden, Théorie approximation, Approximation theory, Variance, Variancia, 60E05, 62E17, 62G30, 62J10, 62Jxx, 65C05, Fonction répartition empirique, Empirical distribution function, Loi Gumbel, Gumbel distribution, 62F10, 62G20, Estimation, Probability plot, Rank regression, Weighted least-squares regression
Document Type:
Academic journal
Article
File Description:
text
Language:
English
Author Affiliations:
Department of Mathematical Statistics and Actuarial Science, University of the Free State, Bloemfontein, South Africa
ISSN:
0361-0918
Rights:
Copyright 2015 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.26164014
Database:
PASCAL Archive
Further Information
Probability plots are often used to estimate the parameters of distributions. Using large sample properties of the empirical distribution function and order statistics, weights to stabilize the variance in order to perform weighted least squares regression are derived. Weighted least squares regression is then applied to the estimation of the parameters of the Weibull, and the Gumbel distribution. The weights are independent of the parameters of the distributions considered. Monte Carlo simulation shows that the weighted least-squares estimators outperform the usual least-squares estimators totally, especially in small samples.