Is the Pareto–Lévy law a good representation of income distributions?

Dagsvik, John K.; Jia, Zhiyang; Vatne, Bjørn Helge; Zhu, Weizhen

doi:10.1007/s00181-011-0539-z

Cited by 7 publications

(7 citation statements)

References 31 publications

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“…This probability distribution is sometimes referred to as Pareto, Inverse Power Law or Pareto‐Lévy (Edwards ; Scafetta ; Dagsvik et al . ).As an alternative model, these step lengths might be generated from Poisson, Negative Exponential, Gaussian or Gamma probability distributions (Gautestad ; Lundy et al . ).…”

Section: The Lévy and Other ‘Random Walks’mentioning

confidence: 97%

“…With a L evy walk, in the absence of resource encounter, different step lengths (l) are assumed to occur with probabilities given by P(l) = al Àl where the exponent l lies within the range 1 < l ≤ 3 and a is a normalizing constant (Viswanathan et al 1999). This probability distribution is sometimes referred to as Pareto, Inverse Power Law or Pareto-L evy (Edwards 2011;Scafetta 2011;Dagsvik et al 2013).As an alternative model, these step lengths might be generated from Poisson, Negative Exponential, Gaussian or Gamma probability distributions (Gautestad 2011(Gautestad , 2013bLundy et al 2013). Other possibilities also exist.…”

Section: The L Evy and Other 'Random Walks'mentioning

confidence: 99%

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Understanding movements of organisms: it's time to abandon the Lévy foraging hypothesis

2014

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Summary1. Interest in Levy walks within the context of movement of organisms has recently soared, with some now referring to this approach as the Levy walk/flight paradigm. The principal assumptions, taken from the world of physics, have been that organisms searching for food or some other resource adopt random walks, whereby the direction of each successive step in the walk is chosen at random from the complete circle and the length of each step, unless terminated through resource encounter, is chosen from a Levy probability distribution with a particular exponent l. The additional assumption that organisms forage optimally, such that l maximizes the rate of resource encounter, has led to the so-called Levy foraging hypothesis, with many attempts to test it. 2. However, the Levy walk model is unrealistic, especially as it omits directionality between successive steps, a typical feature of movements of individual organisms at spatial scales relevant to their movement decisions. It also results in lower foraging efficiency than other more realistic models and the evidence that organisms actually 'do the Levy walk' is weak to non-existent, despite claims to the contrary. Early optimal foraging studies of movements of organisms and a new generation of movement models avoid these problems. 3. It is therefore time to divorce the Levy walk model from optimal foraging theory, revisit some of the early optimal foraging studies of movements and pursue the new generation of movement models. However, the Levy approach may still prove useful at relatively large spatial scales, in terms of both theory and observations, especially in relation to distribution, dispersal and other population-level phenomena, and in this way biology, physics and mathematics may yet work well together.

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Section: The Lévy and Other ‘Random Walks’mentioning

confidence: 97%

Section: The L Evy and Other 'Random Walks'mentioning

confidence: 99%

Understanding movements of organisms: it's time to abandon the Lévy foraging hypothesis

2014

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“…() for a comparison and Clementi and Gallegati (), Dagsvik et al . (), Reed and Fan () or Sarabia et al . () for yet other possibilities.…”

Section: Representing Wealth Distributionsmentioning

confidence: 99%

“…Typical options for income distribution analysis include the log-normal, the gamma distribution (Chakraborti and Patriarca, 2008), the Singh-Maddala (Singh and Maddala, 1976), the Dagum Type I (Dagum, 1977;Kleiber, 2008) or the more flexible Generalized Beta distribution of the Second Kind (McDonald and Ransom, 2008;Jenkins, 2009); see Kleiber and Kotz (2003) for a detailed description of all these distributions, Bandourian et al (2003) for a comparison and Clementi and Gallegati (2005), Dagsvik et al (2013), Reed and Fan (2008) or Sarabia et al (2002) for yet other possibilities. All of these models have however been developed for 'size distributions' and are defined for random variables that take on strictly positive values.…”

Section: Overall Wealth Distributionsmentioning

confidence: 99%

Wealth Inequality: A Survey

Cowell

Kerm

2015

Journal of Economic Surveys

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“…Beta1 and Beta2 are, respectively, the beta of first and second kinds. An alternative three-parameter approach that giving a good representation of income distributions in practice is provided by the Pareto-Lévy class (Mandelbrot 1960, Dagsvik et al 2013; unfortunately, except in a few cases, the probability distributions associated with this class cannot be represented in closed form. Dagum (1977Dagum ( , 1980Dagum ( , 1983, McDonald (1984), Butler and McDonald (1989), Majumder and Chakravarty (1990), McDonald and Xu (1995), Bantilan et al (1995), Victoria-Feser (1995, Brachmann et al (1996), Bordley et al (1997), Tachibanaki et al (1997) and Bandourian et al (2003).…”

Section: Generalized Betamentioning

confidence: 99%