Goroncy, Agnieszka; Rychlik, Tomasz - In: Metrika 78 (2015) 2, pp. 175-204
Assume that <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$X_1,\ldots , X_n$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <msub> <mi>X</mi> <mn>1</mn> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>X</mi> <mi>n</mi> </msub> </mrow> </math> </EquationSource> </InlineEquation> are i.i.d. random variables with a common distribution function <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$F$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>F</mi> </math> </EquationSource> </InlineEquation> which precedes a fixed distribution function <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$W$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>W</mi> </math> </EquationSource> </InlineEquation> in the convex transform order. In particular, if <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$W$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>W</mi> </math> </EquationSource> </InlineEquation> is either uniform or exponential...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>
