This paper proposes a Kolmogorov-type test for the shortfall order (also known in the literature as the right-spread or excess-wealth order) against parametric alternatives. In the case of the null hypothesis corresponding to the Negative Exponential distribution, this provides a test for the...

The revenue ranking of asymmetric auctions with two heterogenous bidders is examined. The main theorem identifies a general environment in which the first-price auction is more profitable than the second-price auction. By using mechanism design techniques, the problem is simplified and several...

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>

Let X1,…,Xn be independent random variables with Xi∼W(α,λi), where W(α,λi) denotes a Weibull distribution with shape parameter α and scale parameter λi, i=1,…,n. Let Y1,…,Yn be a random sample of size n from a Weibull distribution with shape parameter α and a common scale...