Award Date


Degree Type


Degree Name

Master of Science (MS)


Mathematical Sciences

Number of Pages



The Pareto distribution is widely used to describe the distribution of incomes. The distribution can be defined by a location parameter c and a shape parameters a. The maximum likelihood estimators (MLE) and the uniform minimum variance unbiased estimators (UMVUE) for parameters a and c are available in current literature. An improved estimator for parameter a will then be found using a frequentist decision theoretic technique. It is then shown that this improved estimator is the generalized bayes estimator for a certain choice of priors; The Lorenz curve is a tool used to evaluate the share of income of sub-populations or to measure the inequality of individual income distributions. The Lorenz curve for the Pareto distribution will be discussed; The Gini coefficient is a summary measure of the Lorenz curve. The Gini coefficient for the Pareto distribution will be shown to be a function of shape parameter a. The MLE of the Gini coefficient will be discussed. An alternative estimator for the Gini coefficient will then be constructed by using the generalized bayes approach.


Coefficients; Constant; Curve; Distribution; Estimating; Gini; Income; Income Distribution; Lorenz Curve; Pareto Income Distribution

Controlled Subject


File Format


File Size

880.64 KB

Degree Grantor

University of Nevada, Las Vegas




If you are the rightful copyright holder of this dissertation or thesis and wish to have the full text removed from Digital Scholarship@UNLV, please submit a request to and include clear identification of the work, preferably with URL.


IN COPYRIGHT. For more information about this rights statement, please visit