Skewness and Asymmetry: Measures and Orderings

MacGillivray, Helen

doi:10.1214/aos/1176350046

Cited by 160 publications

(56 citation statements)

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“…[3,15,23,35]). In particular, according to Arnold and Groeneveld [3] we can argue that, if F, G are "centered" around the same value (that is, the median in [3], but we can take the mean as well), F is more right asymmetric than G if (1 − p))dp for all t ∈ [0, 1/2].…”

Section: Theorem 3 F (T) = 2t ∀T ∈ [0 1/2] Iff F Is Symmetricmentioning

confidence: 99%

Weak orderings for intersecting Lorenz curves

Lando

Barsotti

2016

METRON

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The Lorenz dominance is a primary tool for comparison of non-negative distributions in terms of inequality. However, in most of cases Lorenz curves intersect and the ordering is not fulfilled, so that some alternative (weaker) criteria need to be to introduced. In this context, the second-degree Lorenz dominance, which emphasizes the role of the left (or right) tail of the distribution, is especially suitable for ranking single-crossing Lorenz curves. We introduce a new ordering, namely disparity dominance, which emphasizes inequality in both of the tails, and we show that, in turn, it is especially suitable for ranking double-crossing Lorenz curves. We argue that the two approaches are basically complementary, although in both cases the Gini coefficient is crucial for the ranking. Moreover, we can use some wellknown results of majorization theory to obtain classes of functionals that are consistent with the aforementioned weak preorders, and that can therefore be used as finer inequality indices.

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Section: Theorem 3 F (T) = 2t ∀T ∈ [0 1/2] Iff F Is Symmetricmentioning

confidence: 99%

Weak orderings for intersecting Lorenz curves

Lando

Barsotti

2016

METRON

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“…In order to avoid LOS parameters which are not meaningful to end-users, the parameters for each distribution are estimated by method of moments, from the mean and variance of LOS. The logarithm of log-normal data is normal-distributed, and the skewness of a normal distribution is 0 due to symmetry [8]. This is not necessarily the case for an Erlang distribution, and so the choice between log-normal or Erlang can be made by comparing the sample skewness of the logarithm of LOS against a threshold value, which we selected as −0.25.…”

Section: Simulation Packagementioning

confidence: 99%

Simulating Bed Capacity: Evaluating the Impact of Healthcare Service Transfers

Bares

Griffiths

Knight

et al. 2012

2012 UKSim 14th International Conference on Computer Modelling and Simulation

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Bed capacity management is an important factor in the effective provision of hospital services. Despite the prevalence of analytical tools suitable for this task, a barrier remains between the techniques available to operational researchers and strategic decision makers. In this paper we introduce a bespoke discrete event simulation package for the analysis of bed usage, which has been developed with a focus on usability and extendibility. A case study is presented for the transfer of Neurosurgery services between two sites, demonstrating the advantages of discrete event simulation over deterministic approaches which do not account for variation in the hospital system.

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“…It is numerically observed that both skewness and kurtosis are decreasing functions of α, moreover, the limiting value of the skewness is approximately 1.139547. The generalized exponential distribution has the MacGillivray [24] skewness function as…”

Section: Density Function and Its Moments Propertiesmentioning

confidence: 99%

Generalized exponential distribution: Existing results and some recent developments

Gupta

Kundu

2007

Journal of Statistical Planning and Inference

258

127

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Mudholkar and Srivastava [25] introduced three-parameter exponentiated Weibull distribution. Two-parameter exponentiated exponential or generalized exponential distribution is a particular member of the exponentiated Weibull distribution. Generalized exponential distribution has a right skewed unimodal density function and monotone hazard function similar to the density functions and hazard functions of the gamma and Weibull distributions. It is observed that it can be used quite effectively to analyze lifetime data in place of gamma, Weibull and log-normal distributions. The genesis of this model, several properties, different estimation procedures and their properties, estimation of the stress-strength parameter, closeness of this distribution to some of the well known distribution functions are discussed in this article.

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Skewness and Asymmetry: Measures and Orderings

Cited by 160 publications

References 0 publications

Weak orderings for intersecting Lorenz curves

Weak orderings for intersecting Lorenz curves

Simulating Bed Capacity: Evaluating the Impact of Healthcare Service Transfers

Generalized exponential distribution: Existing results and some recent developments

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