A characterization of the wald distribution

Suppose X is a random variable having an absolutely continuous distribution function F(x). We assume that F(x) has the Wald distribution. A relation between the probability density function of X⁻¹ with that of X is used to characterize the Wald distribution.     

Quadratic forms in spherical random variables: Generalized noncentral x2 distribution

Let X denote a random vector with a spherically symmetric distribution. The density of U = X'X, called a “generalized chi-square,” is derived for the noncentral case, when μ = E(X) ≠ 0. Explicit series representations are found in certain special cases including the “generalized spherical gamma,” the “generalized” Laplace and the Pearson type VII distributions. A simple geometrical representation of U is shown to be useful in generating random U variates. Expressions for moments and characteristic functions are also given. These densities occur in offset hitting probabilities.     

Book reviews

Exporting Democracy: Fulfilling America's Destiny. By Joshua Muravchik, American Enterprise Institute (1991) ISSN 0–8447–3734–8. $12.95.

Generals in the Palacio. By Roderick Ai Camp. Oxford University Press, (1992), ISBN 0–19–507300–2, £45.

L'Armement en France. Genèse, Ampleur et Coût d'une Industrie By François Chesnais and Claude Serfati, Editions Nathan, Collection Economie/Sciences Sociales, Paris (1992), ISBN 2–09–190086–9.

The Têt Offensive. Intelligence Failure in War. By James Wirtz, Cornell University Press, New York (1991), ISBN 0–8014–2486–0. $38.50.

Restructuring of arms producton in Western Europe. Edited by Michael Brzoska and Peter Lock. Oxford University Press, Oxford (1992), ISBN 0–1982–9147–7. £25.00.

What is Proper Soldiering? A study of new perspectives for the future uses of the Armed Forces of the 1990s. By Michael Harbottle. The Centre for International Peacebuilding, Chipping Norton (1992), £3.50.

The Strategic Defence Initiative By Edward Reiss, Cambridge University Press, Cambridge (1992), ISBN 0–521–41097–5. £30.00.     

On estimating survival for reliability models based on age-related stochastic comparisons

A new class of nonparametric reliability models is introduced and studied. A distribution is said to be better at age s than at age t (sBt) if the residual lifetime at age s is stochastically greater than or equal to the residual lifetime at age t. Applications to various forms of replacement policies, including the cannibalization of failed systems, are noted. For fixed s < t, the problem of estimating a survival curve assumed to belong to the sBt class is addressed using recursive methods. An sBt estimator is derived in closed form, and its uniform strong consistency at an optimal rate of convergence is demonstrated. A simulation study strongly supports the claim that the sBt estimator tends to outperform the empirical survivor function in small- and moderate-size samples. © 1993 John Wiley & Sons, Inc.     

A higher order coupled frequency characteristics study of smartmagneto-electro-elastic composite plates with cut-outs using finite element methods

This article deals with investigating the effect of cut-outs on the natural frequencies of magneto-electro-elastic (MEE) plates incorporating finite element methods based on higher order shear deformation theory (HSDT). In order to consider the influence of cut-out, the energy of the cut-out domain is sub-tracted from the total energy of the entire plate. The governing equations of motions are derived through incorporating Hamilton's principle and the solution is obtained using condensation technique. The proposed numerical formulation is verified with the results of previously published literature as well as the numerical software. In addition, this research focuses on evaluating the effect of geometrical skewness and boundary conditions on the frequency response. The influence of cut-outs on the degree of coupling between magnetic, electric and elasticfields is also investigated.     

Damage mechanics and energy absorption capabilities of naturalfiber reinforced elastomeric based bio composite for sacrificial structural applications

The present study deals with the experimental, finite element (FE) and analytical assessment of low ballistic impact response of proposedflexible'green' composite make use of naturally available jute and rubber as the constituents of the composite with stacking sequences namely jute/rubber/jute (JRJ), jute/rubber/rubber/jute (JRRJ) and jute/rubber/jute/rubber/jute (JRJRJ). Ballistic impact tests were carried out by firing a conical projectile using a gas gun apparatus at lower range of ballistic impact regime. The ballistic impact response of the proposed flexible composites are assesses based on energy absorption and damage mechanism. Results revealed that inclusion of natural rubber aids in better energy ab-sorption and mitigating the failure of the proposed composite. Among the three different stacking se-quences of flexible composites considered, JRJRJ provides better ballistic performance compared to its counterparts. The damage study reveals that the main mechanism of failure involved in flexible com-posites is matrix tearing as opposed to matrix cracking in stiff composites indicating that the proposedflexible composites are free from catastrophic failure. Results obtained from experimental, FE and analytical approach pertaining to energy absorption and damage mechanism agree well with each other. The proposed flexible composites due to their exhibited energy absorption capabilities and damage mechanism are best suited as claddings for structural application subjected to impact with an aim of protecting the main structural component from being failed catastrophically.     

The Demand for Military Spending in Egypt

Egypt plays a pivotal role in the security of the Middle East as the doorway to Europe and its military expenditure reflects its involvement in the machinations of such an unstable region, showing considerable variation over the last 40?years. These characteristics make it a particularly interesting case study of the determinants of military spending. This paper specifies and estimates an econometric model of the Egyptian demand for military spending, taking into account important strategic and political factors. Both economic and strategic factors are found to play a role in determining military burden/spending, with clear positive effects of lagged military burden, suggesting some sort of institutional inertia, plus negative output and net exports effects. The strategic effect as a result of the impact of Israel’s military burden is mostly positive and significant, though its impact is reduced when the impact of important strategic events are taken into account. The military spending of Egypt’s allies Jordan and Syria generally seems to have had no effect on Egypt’s spending. These results are consistent over a range of econometric techniques.