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Suppose we have k samples X₁,₁,…,X₁,ₙ₁,…,Xₖ,₁,…,Xₖ,ₙₖ with different sample sizes ₙ₁,…,ₙₖ and unknown underlying distribution functions F₁,…,Fₖ as observations plus k families of distribution functions {G₁(⋅,ϑ);ϑ∈Θ},…,{Gₖ(⋅,ϑ);ϑ∈Θ}, each indexed by elements ϑ from the same parameter set Θ, we consider the new goodness-of-fit problem whether or not (F₁,…,Fₖ) belongs to the parametric family {(G₁(⋅,ϑ),…,Gₖ(⋅,ϑ));ϑ∈Θ}. New test statistics are presented and a parametric bootstrap procedure for the approximation of the unknown null distributions is discussed. Under regularity assumptions, it is proved that the approximation works asymptotically, and the limiting distributions of the test statistics in the null hypothesis case are determined. Simulation studies investigate the quality of the new approach for small and moderate sample sizes. Applications to real-data sets illustrate how the idea can be used for verifying model assumptions.
A hybrid-electric propulsion system combines the advantages of fuel-based systems and battery powered systems and offers new design freedom. To take full advantage of this technology, aircraft designers must be aware of its key differences, compared to conventional, carbon-fuel based, propulsion systems. This paper gives an overview of the challenges and potential benefits associated with the design of aircraft that use hybrid-electric propulsion systems. It offers an introduction of the most popular hybrid-electric propulsion architectures and critically assess them against the conventional and fully electric propulsion configurations. The effects on operational aspects and design aspects are covered. Special consideration is given to the application of hybrid-electric propulsion technology to both unmanned and vertical take-off and landing aircraft. The authors conclude that electric propulsion technology has the potential to revolutionize aircraft design. However, new and innovative methods must be researched, to realize the full benefit of the technology.
The paper deals with an asymptotic relative efficiency concept for confidence regions of multidimensional parameters that is based on the expected volumes of the confidence regions. Under standard conditions the asymptotic relative efficiencies of confidence regions are seen to be certain powers of the ratio of the limits of the expected volumes. These limits are explicitly derived for confidence regions associated with certain plugin estimators, likelihood ratio tests and Wald tests. Under regularity conditions, the asymptotic relative efficiency of each of these procedures with respect to each one of its competitors is equal to 1. The results are applied to multivariate normal distributions and multinomial distributions in a fairly general setting.
Laser-based Additive Manufacturing (AM) processes for the use of metals out of the powder bed have been investigated profusely and are prevalent in industry. Although there is a broad field of application, Laser Powder Bed Fusion (LPBF), also known as Selective Laser Melting (SLM) of glass is not fully developed yet. The material properties of glass are significantly different from the investigated metallic material for LPBF so far. As such, the process cannot be transferred, and the parameter limits and the process sequence must be redefined for glass. Starting with the characterization of glass powders, a parameter field is initially confined to investigate the process parameter of different glass powder using LPBFprocess. A feasibility study is carried out to process borosilicate glass powder. The effects of process parameters on the dimensional accuracy of fabricated parts out of borosilicate and hints for the post-processing are analysed and presented in this paper.