Estimation in the Presence of Measurement Errors: Estimation of Pareto Distribution Functions from Samples Contaminated by Measurement Errors

This study considers the problem of estimating the population distribution of independent random variables from error-contaminated samples. 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. 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.