In this paper we study convolution residuals, that is, if <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$X_1,X_2,\ldots ,X_n$$</EquationSource> </InlineEquation> are independent random variables, we study the distributions, and the properties, of the sums <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$\sum _{i=1}^lX_i-t$$</EquationSource> </InlineEquation> given that <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$\sum _{i=1}^kX_it$$</EquationSource> </InlineEquation>, where <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$t\in \mathbb R $$</EquationSource> </InlineEquation>, and <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$$1\le k\le l\le n$$</EquationSource> </InlineEquation>....</equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation>

Modular decomposition is a thoroughly investigated topic in many areas such as switching theory, reliability theory, game theory and graph theory. Most appli- cations can be formulated in the framework of Boolean functions. In this paper we give a uni_ed treatment of modular decomposition of...

Many products carry a warranty that offers protection for the consumer against low quality. These warranties are often two dimensional, such as an automobile warranty that guarantees repair up to a certain time and mileage after sale. This paper considers the problem of assessing the size of a...

Kovenock and Roberson’s (2012ab) replication of Hausken’s (2008a) equations and parameter restrictions do not enhance our insight into the defense and attack of reliability systems. This reply intends to fill the remaining understanding gaps.

A system of two components is analyzed as a two-period game. After period 1 the system can be fully operational, in two states of intermediate degradation, or fail. Analogously to changing failure rates in dependent systems analyzed with Markov analysis, unit costs of defense and attack, and...

Modular decomposition is a thoroughly investigated topic in many areas such as switching theory, reliability theory, game theory and graph theory. Most appli- cations can be formulated in the framework of Boolean functions. In this paper we give a uni_ed treatment of modular decomposition of...

Hausken (2008a) formulates a contest-theoretic model of the attack and defense of a network of targets. This note identies a technical error that invalidates Hausken's characterization of Nash equilibrium for a substantial portion of the parameter space that he examines and provides necessary...

Kovenock and Roberson’s (2010) paper has the potential to advance the research frontier, but has deficiencies. This paper suggests how Kovenock and Roberson’s (2010) paper can be developed into a more substantial paper. Kovenock and Roberson’s (2010) paper consists of three sections. The...

We provide a sufficient condition for a mixture of Beta distributions to have log-concave density. This is true whenever the Beta distributions to be mixed together have constant parameter sum and the mixing weights are themselves log-concave. The result has applications in economics and...