Recovery of a quantile function from moments

The problem of recovering a quantile function of a positive random variable via the values of moments or given the values of its Laplace transform is studied. Two new approximations as well as two new estimates of a quantile function given the sample from underlying distribution are proposed. The un...

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Veröffentlicht in:	Journal of computational and applied mathematics 2017-05, Vol.315, p.354-364
Hauptverfasser:	Mnatsakanov, Robert M., Sborshchikovi, Aleksandre
Format:	Artikel
Sprache:	eng
Schlagworte:	Applications of mathematics Approximation Estimates Laplace transform inversion Laplace transforms Mathematical analysis Mathematical models Moment-recovered approximation Quantile function Quantiles The Lorenz curve Upper bounds
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Beschreibung
Zusammenfassung:	The problem of recovering a quantile function of a positive random variable via the values of moments or given the values of its Laplace transform is studied. Two new approximations as well as two new estimates of a quantile function given the sample from underlying distribution are proposed. The uniform and L1 upper bounds of proposed estimates are derived. The plots illustrate the behavior of the recovered approximants for the moderate and large sample sizes.
ISSN:	0377-0427 1879-1778
DOI:	10.1016/j.cam.2016.11.028