Estimation of Pareto distribution functions from samples contaminated by measurement errors
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Date
2010
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
University of the Western Cape
Abstract
The intention is to draw more specific connections between certain deconvolution methods and also to demonstrate the application of the statistical theory of estimation in the presence of measurement error. A parametric methodology for deconvolution when the underlying distribution is of the Pareto form is developed. Maximum likelihood estimation (MLE) of the parameters of the convolved distributions is considered. Standard errors of the estimated parameters are calculated from the inverse Fisher’s information matrix and a jackknife method. Probability-probability (P-P) plots and Kolmogorov-Smirnov (K-S) goodnessof- fit tests are used to evaluate the fit of the posited distribution. A bootstrapping method is used to calculate the critical values of the K-S test statistic, which are not available.
Description
Magister Scientiae - MSc
Keywords
Deconvolution, Distribution functions, Error-Contaminated samples, Errors-in-variables, Jackknife, Maximum likelihood method, Measurement errors, Nonparametric estimation, Pareto distribution