Stochastic dominance relations for generalised parametric distributions obtained through composition

Tommaso Lando () and Lucio Bertoli-Barsotti
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Tommaso Lando: University of Bergamo
Lucio Bertoli-Barsotti: University of Bergamo

METRON, 2020, vol. 78, issue 3, No 3, 297-311

Abstract: Abstract Investigating stochastic dominance within flexible multi-parametric families of distributions is often complicated, owing to the high number of parameters or non-closed functional forms. To simplify the problem, we use the T–X method, making it possible to obtain generalised models through the composition of cumulative distributions and quantile functions. We derive conditions for the second-order stochastic dominance and for the increasing convex order within multi-parametric families in two steps, namely: (i) breaking them down via the T–X approach and (ii) checking dominance conditions of the (more) manageable distributions composing the model. We apply our method to some special distributions and focus on the beta-generated family, which enables the comparisons of order statistics of i.i.d. samples from (possibly) different random variables.

Keywords: Stochastic dominance; T–X family; Generalised distributions; Generalised beta; Order statistics; 60E15; 62XX; 60E05 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s40300-020-00184-4

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