Traditional shock models view system failure time as a first passage problem. Yeh Lam proposed a new class of models called δ-shock models in which failure was dependent on the frequency of shocks. The present work generalizes Yeh Lam's results for renewal shock arrivals and random threshold....

In state legislative elections some candidates attract contributions from many donors whereas other candidates have much smaller donor pools. Why? What are the origins of these disparities? This paper conceptualizes contributions as a type of attachment between the donor and the state...

Significant differences in the evolution of firm size distribution for various industries in the United States have been revealed and documented. For theoretical considerations, this finding puts major constraints on the modelling of firm growth. For practical purposes, the observed differences...

This work presents a simple method for calculating deviations regarding city size and the size which would correspond to it with a Pareto exponent equal to one unit (Zipf’s Law). Recent works show that when considering the entire sample without size restrictions, the estimated Pareto exponent...

We consider a problem of characterization of continuous distributions for which linearity of regression of overlapping order statistics, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\mathbb {E}(X_{i:m}|X_{j:n})=aX_{j:n}+b$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi mathvariant="double-struck">E</mi> <mrow> <mo stretchy="false">(</mo> <msub> <mi>X</mi> <mrow> <mi>i</mi> <mo>:</mo> <mi>m</mi> </mrow> </msub> <mo stretchy="false">|</mo> <msub> <mi>X</mi> <mrow> <mi>j</mi> <mo>:</mo> <mi>n</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mi>a</mi> <msub> <mi>X</mi> <mrow> <mi>j</mi> <mo>:</mo> <mi>n</mi> </mrow> </msub> <mo>+</mo> <mi>b</mi> </mrow> </math> </EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$m\le n$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mrow> <mi>m</mi> <mo>≤</mo> <mi>n</mi> </mrow> </math> </EquationSource> </InlineEquation>, holds. Due to a new...</equationsource></equationsource></inlineequation></equationsource></equationsource></inlineequation>