Estimation of Pareto Distribution Functions from Samples Contaminated by Measurement Errors

dc.contributor.advisorKoen, Chris
dc.contributor.authorKondlo, Lwando Orbet
dc.date.accessioned2022-03-07T10:15:17Z
dc.date.accessioned2024-05-14T09:53:15Z
dc.date.available2022-03-07T10:15:17Z
dc.date.available2024-05-14T09:53:15Z
dc.date.issued2010
dc.description>Magister Scientiae - MScen_US
dc.description.abstractEstimation of population distributions, from samples that are contaminated by measurement errors, is a common problem. This study considers the problem of estimating the population distribution of independent random variables Xi, from error-contaminated samples ~i (.j = 1, ... , n) such that Yi = Xi + f·.i, where E is the measurement error, which is assumed independent of X. The measurement error ( is also assumed to be normally distributed. Since the observed distribution function is a convolution of the error distribution with the true underlying distribution, estimation of the latter is often referred to as a deconvolution problem. A thorough study of the relevant deconvolution literature in statistics is reported. We also deal with the specific case when X is assumed to follow a truncated Pareto form. If observations are subject to Gaussian errors, then the observed Y is distributed as the convolution of the finite-support Pareto and Gaussian error distributions. The convolved probability density function (PDF) and cumulative distribution function (CDF) of the finite-support Pareto and Gaussian distributions are derived. The intention is to draw more specific connections bet.ween 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. Simulated data are used to validate the methodology. A real-life application of the methodology is illustrated by fitting convolved distributions to astronomical dataen_US
dc.identifier.urihttps://hdl.handle.net/10566/14911
dc.language.isoenen_US
dc.publisherUniversity of the Western Capeen_US
dc.rights.holderUniversity of the Western Capeen_US
dc.subjectDeconvolutionen_US
dc.subjectDistribution functionsen_US
dc.subjectError-Contaminated samplesen_US
dc.subjectErrors-in-variablesen_US
dc.subjectJackknifeen_US
dc.subjectMaximum likelihood methoden_US
dc.subjectMeasurement errorsen_US
dc.subjectNonparametrie estimationen_US
dc.subjectPareto distributionen_US
dc.titleEstimation of Pareto Distribution Functions from Samples Contaminated by Measurement Errorsen_US

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