Using Order Statistics Distribution Functions in Modeling Grouped Data for Pareto Distribution | ||
| The Egyptian Statistical Journal | ||
| Article 6, Volume 37, Issue 2, December 1993, Pages 238-250 | ||
| Document Type: Original Article | ||
| DOI: 10.21608/esju.1993.314843 | ||
| Authors | ||
| Wafik Youssef Younan; Maged George Iskander | ||
| Abstract | ||
| The main purpose of this article is to use order statistics like distribution functions to model grouped data such as the grouped data for income. Initially, the one parameter Pareto distribution is fitted to the data. Then by using arbitrarily chosen pairs (n, r) of positive values as extra parameters (with n ≥ r) a class of models (a collection of distribution functions) is introduced from which a simple suitable mathematical model is chosen. Each of these models represents the distribution function like that of the rth order statistic in a random sample of size n. The parameter of the Pareto distribution is estimated by maximum likelihood method while a numerical search is carried out to provide a model that fits the data better. This process continues till the " best" values of n and r are obtained and the corresponding model is the best fit to the data. A numerical example, based on a hypothetical set of grouped data is given to show the advantage of the suggested technique in improving the data modeling. | ||
| Keywords | ||
| Distribution Functions; Grouped Data Modeling; Maximum Likelihood Estimation; Order Statistics; Pareto distribution | ||
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