$L$-functions, processes, and statistics in measuring economic inequality and actuarial risks
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In this paper, the authors analyzed a data set from the Bank of Italy year 2006 sample survey on household budgets and introduced the L-process on which statistical inferential results about the population L-function hinges.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.read more
Citations
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Zenga's new index of economic inequality, its estimation, and an analysis of incomes in Italy.
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References
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BookDOI
Density estimation for statistics and data analysis
TL;DR: The Kernel Method for Multivariate Data: Three Important Methods and Density Estimation in Action.
Journal ArticleDOI
On the Measurement of Inequality
TL;DR: In this paper, the problem of comparing two frequency distributions f(u) of an attribute y which for convenience I shall refer to as income is defined as a risk in the theory of decision-making under uncertainty.
Book
Approximation Theorems of Mathematical Statistics
TL;DR: In this paper, the basic sample statistics are used for Parametric Inference, and the Asymptotic Theory in Parametric Induction (ATIP) is used to estimate the relative efficiency of given statistics.
Book
On Economic Inequality
Amartya Sen,James E. Foster +1 more
TL;DR: In this paper, Amartya Sen relates the theory of welfare economics to the study of economic inequality and presents a systematic treatment of the conceptual framework as well as the practical problems of measurement of inequality.