The representation of the entropy in terms of the hazard function and its extensions have been studied by many authors including Teitler et al. (IEEE Trans Reliab 35:391–395, <CitationRef CitationID="CR16">1986</CitationRef>). In this paper, we consider a representation of the Kullback–Leibler information of the first <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$r$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>r</mi> </math> </EquationSource> </InlineEquation>...</equationsource></equationsource></inlineequation></citationref>

Some extensions of entropy and KL information to the survival function have been recently proposed. We first compare some extensions of KL information and provide a criterion in choosing one among those extensions. Then we study moment constraints for maximum cumulative residual entropy...

Computer simulations are often used to replace physical experiments for exploring the complex relationships between input and output variables. We study the optimal design problem for the prediction of a stationary Ornstein–Uhlenbeck sheet on a monotonic set with respect to the integrated mean...

Two of the present authors have put forward a projective geometry based model of rational trading that implies a model for subjective demand/supply profiles if one considers closing of a position as a random process. We would like to present the analysis of a subjectivity in such trading models....