Madan L. Puri

Bio: Madan L. Puri is an academic researcher from University of Texas at Arlington. The author has contributed to research in topics: Simple random sample & Risk measure. The author has an hindex of 1, co-authored 1 publications receiving 57 citations.

$L$-functions, processes, and statistics in measuring economic inequality and actuarial risks

Abstract: L-statistics play prominent roles in various research areas and applications, including development of robust statistical methods, measuring economic inequality and insurance risks. In many applications the score functions of L-statistics depend on parameters (e.g., distortion parameter in insurance, risk aversion parameter in econometrics), which turn the L-statistics into functions that we call L-functions. A simple example of an L-function is the Lorenz curve. Ratios of L-functions play equally important roles, with the Zenga curve being a prominent example. To illustrate real life uses of these functions/curves, we analyze a data set from the Bank of Italy year 2006 sample survey on household budgets. Naturally, empirical counterparts of the population L-functions need to be employed and, importantly, adjusted and modified in order to meaningfully capture situations well beyond those based on simple random sampling designs. In the processes of our investigations, we also introduce the L-process on which statistical inferential results about the population L-function hinges. Hence, we provide notes and references facilitating ways for deriving asymptotic properties of the L-process.

Weighted Pricing Functionals With Applications to Insurance

Abstract: We explore the role of weighted distributions in pricing insurance risks. In particular, we relate the distributions to actuarial and economic premium calculation principles and in this way provide a unifying methodology for constructing new principles and analyzing known ones.

Is the Gini Index of Inequality Overly Sensitive to Changes in the Middle of the Income Distribution

Abstract: The Gini index is the most commonly used measure of income inequality. Like any single summary measure of a set of data, it cannot capture all aspects that are of interest to researchers. One of its widely reported flaws is that it is supposed to be overly sensitive to changes in the middle of the distribution. By studying the effect of small transfers between households or an additional increment in income going to one member of the population on the value of the index, this claim is re-examined. It turns out that the difference in the rank order of donor and recipient is usually the most important factor determining the change in the Gini index due to the transfer, which implies that transfers from an upper income household to a low income household receive more weight that transfers involving the middle. Transfers between two middle-income households do affect a higher fraction of the population than other transfers but those transfers do not receive an excessive weight relative to other transf...

Zenga's new index of economic inequality, its estimation, and an analysis of incomes in Italy.

Abstract: For at least a century academics and governmental researchers have been developing measures that would aid them in understanding income distributions, their differences with respect to geographic regions, and changes over time periods. It is a fascinating area due to a number of reasons, one of them being the fact that different measures, or indices, are needed to reveal different features of income distributions. Keeping also in mind that the notions of poor and rich are relative to each other, Zenga (2007) proposed a new index of economic inequality. The index is remarkably insightful and useful, but deriving statistical inferential results has been a challenge. For example, unlike many other indices, Zenga's new index does not fall into the classes of -, -, and -statistics. In this paper we derive desired statistical inferential results, explore their performance in a simulation study, and then use the results to analyze data from the Bank of Italy Survey on Household Income and Wealth (SHIW).