The Atkinson Index, the Moran Statistic, and Testing Exponentiality

Mimoto, Nao; Zitikis, Ričardas

doi:10.14490/jjss.38.187

Cited by 23 publications

(13 citation statements)

References 29 publications

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“…This leads us to solve: Table 1 shows the eigenvalues of the asymptotic covariance matrix of T m and the corresponding constants, a, b, and ν for m = 1, 2, 3 and 4. Table 2 shows the critical points, obtained by simulation, for the T m statistics (m = 0, 1, 2, 3 and 4) for samples of size 50, 100, 200, 500, 1000 and 2000, corresponding to the 90, 95 and 99 percentiles, as well as the values obtained by simulation of the asymptotic distribution (8) and the approximation given from (11). The simulations are all run with 50, 000 samples.…”

Section: Approximate Critical Pointsmentioning

confidence: 99%

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Methods to Distinguish Between Polynomial and Exponential Tails

Castillo¹,

Daoudi

Lockhart

2014

Scandinavian J Statistics

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Two methods to distinguish between polynomial and exponential tails are introduced. The methods are based on the properties of the residual coefficient of variation for the exponential and non-exponential distributions. A graphical method, called a CV-plot, shows departures from exponentiality in the tails. The plot is applied to the daily log-returns of exchange rates of US dollar and Japanese yen. New statistics are introduced for testing the exponentiality of tails using multiple thresholds. They give better control of the significance level than previous tests. The powers of the new tests are compared with those of some others for various sample sizes.

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Section: Approximate Critical Pointsmentioning

confidence: 99%

“…Lee et al (1980) and Ascher (1990) discuss tests based on the equation E (X p ) /E (X) p = Γ (1 + p), for some p > 0, where X is an exponential random variable. The limit case, when p tends to 0, is studied in Mimoto and Zitikis (2008), see also references therein. The case p = 2 is equivalent to the coefficient of variation test.…”

Section: Introductionmentioning

confidence: 99%

Methods to Distinguish Between Polynomial and Exponential Tails

Castillo¹,

Daoudi

Lockhart

2014

Scandinavian J Statistics

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“…In addition, Mimoto and Zitikis (2008) have found the Atkinson index useful for developing a statistical inference theory for testing exponentiality, which has been a prominent problem in life-time analysis and, particularly, in reliability engineering.…”

Section: From the Mean To Generic Societal Referencesmentioning

confidence: 99%

From the Classical Gini Index of Income Inequality to a New Zenga-Type Relative Measure of Risk: A Modeller’s Perspective

Greselin

Zitikis

2018

Econometrics

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Abstract:The underlying idea behind the construction of indices of economic inequality is based on measuring deviations of various portions of low incomes from certain references or benchmarks, which could be point measures like the population mean or median, or curves like the hypotenuse of the right triangle into which every Lorenz curve falls. In this paper, we argue that, by appropriately choosing population-based references (called societal references) and distributions of personal positions (called gambles, which are random), we can meaningfully unify classical and contemporary indices of economic inequality, and various measures of risk. To illustrate the herein proposed approach, we put forward and explore a risk measure that takes into account the relativity of large risks with respect to small ones.

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“…This index has been highly influential in measuring economic inequality (cf., e.g., Cowell, 2011, and references therein) and inspired a variety of extensions and generalization of the Gini index; we shall say more on this in the next section. Furthermore, Mimoto & Zitikis (2008) have found the Atkinson index useful in developing a statistical inference theory for testing exponentiality, which has been a prominent problem in life-time analysis and particularly in reliability engineering.…”

Section: Atkinson Indexmentioning

confidence: 99%

Measuring Economic Inequality and Risk: A Unifying Approach Based on Personal Gambles, Societal Preferences and References

Greselin

Zitikis

2015

SSRN Journal

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The underlying idea behind the construction of indices of economic inequality is based on measuring deviations of various portions of low incomes from certain references or benchmarks, that could be point measures like population mean or median, or curves like the hypotenuse of the right triangle where every Lorenz curve falls into. In this paper we argue that by appropriately choosing population-based references, called societal references, and distributions of personal positions, called gambles, which are random, we can meaningfully unify classical and contemporary indices of economic inequality, as well as various measures of risk. To illustrate the herein proposed approach, we put forward and explore a risk measure that takes into account the relativity of large risks with respect to small ones.

show abstract

The Atkinson Index, the Moran Statistic, and Testing Exponentiality

Cited by 23 publications

References 29 publications

Methods to Distinguish Between Polynomial and Exponential Tails

Methods to Distinguish Between Polynomial and Exponential Tails

From the Classical Gini Index of Income Inequality to a New Zenga-Type Relative Measure of Risk: A Modeller’s Perspective

Measuring Economic Inequality and Risk: A Unifying Approach Based on Personal Gambles, Societal Preferences and References

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