On a New Measure of Skewness for Unimodal Distributions

Das, Shubhabratha; Ghosh, Diptesh

doi:10.2139/ssrn.2157417

Cited by 2 publications

(4 citation statements)

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“…According to Das et al . (), F 1 is a homogeneously right‐skewed distribution, and so μ cannot be chosen as an appropriate central value θ , because of the negative value of

S_{μ}^{-} (F_{1})

. However, when mode M is used as a central value,

S_{M}^{-} (F_{1}) = 0

indicates no left skewness (Figure , dotted line).…”

Section: Measuring Positive and Negative Skewnessmentioning

confidence: 99%

“…The idea of studying the skewness of a distribution by means of a function is found, for instance, in Das et al . (), where the skewness function is defined as

γ_{f} (x) = f (M + x) - f (M - x), x > 0 .

…”

Section: Introductionmentioning

confidence: 99%

“…Following Das et al . (), where the values

\int_{γ_{f} > 0} |γ_{f} (x)| dx, \int_{γ_{f} < 0} |γ_{f} (x)| dx

areevaluated and compared to obtain a single index, we introduce a functional map, which can be examined as a local function for the purpose of measuring skewness.…”

Section: Introductionmentioning

confidence: 99%

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Complementary information for skewness measures

García

Martel

Polo

2015

Statistica Neerlandica

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This paper introduces some new elements to measure the skewness of a probability distribution, suggesting that a given distribution can have both positive and negative skewness, depending on the centred sub‐interval of the support set being observed. A skewness function for positive reals is defined, from which a bivariate index of positive–negative skewness is obtained. Certain interesting properties of this new index are studied, and they are also obtained for some common discrete distributions. We show the advantages of their use as a complement to the information derived by traditional measures of skewness.

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“…According to Das et al . (), F 1 is a homogeneously right‐skewed distribution, and so μ cannot be chosen as an appropriate central value θ , because of the negative value of

S_{μ}^{-} (F_{1})

. However, when mode M is used as a central value,

S_{M}^{-} (F_{1}) = 0

indicates no left skewness (Figure , dotted line).…”

Section: Measuring Positive and Negative Skewnessmentioning

confidence: 99%

“…The idea of studying the skewness of a distribution by means of a function is found, for instance, in Das et al . (), where the skewness function is defined as

γ_{f} (x) = f (M + x) - f (M - x), x > 0 .

…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Complementary information for skewness measures

García

Martel

Polo

2015

Statistica Neerlandica

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show abstract

“…Many authors have proposed and obtained different descriptive elements to measure skewness (see, for instance, [8][9][10][11][12][13]). Ref [10] suggested a measurement of skewness corresponding to the (unique) mode, M, given by the following index:…”

Section: Introductionmentioning

confidence: 99%

A Note on Ordering Probability Distributions by Skewness

2018

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This paper describes a complementary tool for fitting probabilistic distributions in data analysis. First, we examine the well known bivariate index of skewness and the aggregate skewness function, and then introduce orderings of the skewness of probability distributions. Using an example, we highlight the advantages of this approach and then present results for these orderings in common uniparametric families of continuous distributions, showing that the orderings are well suited to the intuitive conception of skewness and, moreover, that the skewness can be controlled via the parameter values.

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On a New Measure of Skewness for Unimodal Distributions

Cited by 2 publications

References 0 publications

Complementary information for skewness measures

Complementary information for skewness measures

A Note on Ordering Probability Distributions by Skewness

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