On Iterated Lorenz Curves with Applications
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914144639254528 |
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| author | Ignatov, Zvetan Yordanov, Vilimir |
| author_facet | Ignatov, Zvetan Yordanov, Vilimir |
| contents | It is well known that a Lorenz curve, derived from the distribution function of a random variable, can itself be viewed as a probability distribution function of a new random variable (Arnold, 2015). We prove the surprising result that a sequence of consecutive iterations of this map leads to a non-corner case convergence, independent of the initial random variable. In the primal case, both the limiting distribution and its parent follow a power-law distribution with exponent equal to the golden section. In the reflected case, the limiting distribution is the Kumaraswamy distribution with a conjugate value of the exponent, while the parent distribution is the classical Pareto distribution. Potential applications are also discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_13183 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Iterated Lorenz Curves with Applications Ignatov, Zvetan Yordanov, Vilimir Probability 39B12, 60F99, 62G30, 62G32, 62P05 It is well known that a Lorenz curve, derived from the distribution function of a random variable, can itself be viewed as a probability distribution function of a new random variable (Arnold, 2015). We prove the surprising result that a sequence of consecutive iterations of this map leads to a non-corner case convergence, independent of the initial random variable. In the primal case, both the limiting distribution and its parent follow a power-law distribution with exponent equal to the golden section. In the reflected case, the limiting distribution is the Kumaraswamy distribution with a conjugate value of the exponent, while the parent distribution is the classical Pareto distribution. Potential applications are also discussed. |
| title | On Iterated Lorenz Curves with Applications |
| topic | Probability 39B12, 60F99, 62G30, 62G32, 62P05 |
| url | https://arxiv.org/abs/2401.13183 |