A test for the hypothesis that two extreme-value scale parameters are equal

A statistic is determined for testing the hypothesis of equality for scale parameters from two populations, each of which has the first asymptotic distribution of smallest (extreme) values. The probability distribution is derived for this statistic, and critical values are determined and given in tabular form for a one-sided or two-sided alternative, for censored samples of size n₁ and n₂, n₁ = 2, 3, …. 6, n₂ = 2, 3, …. 6. The power function of the test for certain alternatives is also calculated and listed in each case considered.     

An F approximation for two-parameter weibull and log-normal tolerance bounds based on possibly censored data

An approximation suggested in Mann, Schafer and Singpurwalla [18] for obtaining small-sample tolerance bounds based on possibly censored two-parameter Weibull and lognormal samples is investigated. The tolerance bounds obtained are those that effectively make most efficient use of sample data. Values based on the approximation are compared with some available exact values and shown to be in surprisingly good agreement, even in certain cases in which sample sizes are very small or censoring is extensive. Ranges over which error in the approximation is less than about 1 or 2 percent are determined. The investigation of the precision of the approximation extends results of Lawless [8], who considered large-sample maximum-likelihood estimates of parameters as the basis for approximate 95 percent Weibull tolerance bounds obtained by the general approach described in [18]. For Weibull (or extreme-value) data the approximation is particularly useful when sample sizes are moderately large (more than 25), but not large enough (well over 100 for severely censored data) for asymptotic normality of estimators to apply. For such cases simplified efficient linear estimates or maximum-likelihood estimates may be used to obtain the approximate tolerance bounds. For lognormal censored data, best linear unbiased estimates may be used, or any efficient unbiased estimators for which variances and covariances are known as functions of the square of the distribution variance.     

Weibull tolerance intervals associated with moderate to small survival proportions for use in a new formulation of lanchester combat theory

Given herein is an easily implemented method for obtaining, from complete or censored data, approximate tolerance intervals associated with the upper tail of a Weibull distribution. These approximate intervals are based on point estimators that make essentially most efficient use of sample data. They agree extremely well with exact intervals (obtained by Monte Carlo simulation procedures) for sample sizes of about 10 or larger when specified survival proportions are sufficiently small. Ranges over which the error in the approximation is within 2 percent are determined. The motivation for investigation of the methodology for obtaining the approximate tolerance intervals was provided by the new formulation of Lanchester Combat Theory by Grubbs and Shuford [3], which suggests a Weibull assumption for time-to-incapacitation of key targets. With the procedures investigated herein, one can use (censored) data from battle simulations to obtain confidence intervals on battle times associated with given low survivor proportions of key targets belonging to either specified side in a future battle. It is also possible to calculate confidence intervals on a survival proportion of key targets corresponding to a given battle duration time.     

INTERNATIONAL SECURITY ON THE ROAD TO NUCLEAR ZERO

The disappointingly slow pace of progress on efforts to prevent proliferation, reduce nuclear weapons, and eliminate nuclear risks has many causes. The factor that might be easiest for individuals in the arms control and nonproliferation community to change stems from their own ambivalence about major questions that must be addressed on the road to reducing the number of nuclear weapons in the world to zero. This essay explores how ambivalence about four key issues—strategic stability, alliance relations, institution-building, and nuclear energy—often leads community members to take positions that play well at home and within their like-minded group but raise unintended impediments to achieving their own long-term goals. The author suggests alternative ways to handle these questions to improve the prospects for domestic and international agreement on practical measures that would eliminate, not perpetuate, nuclear risks.     

Terrorism in Nigeria

Using the Boko Haram terrorist group in Nigeria as a point of departure, this paper examines the implications of the operations of terrorist groups on the security and stability of states in West Africa. It predominantly utilises secondary sources of data. Findings indicate that the membership and operations of this terrorist group are spreading across the sub-region. This spread is consequent upon Boko Haram's collaboration with other terrorist groups within West Africa and beyond. This constitutes threats to the security and stability of states in the sub-region. Thus, the paper recommends, among other things: a thorough understanding of the operational strategies of terrorist groups by states and those involved in security policymaking in the sub-region; and for agreements to be reached among Economic Community of West African States (ECOWAS) member states and their governments for collaboration in various areas in order to curtail transnational crime and terrorism, and reduce socio-economic inequality that generates aggressive behaviours among the less privileged.     

Re-thinking the Unthinkable: Arms Control in the Twenty-First Century

ABSTRACT

Since the end of the Cold War, arms control proponents tried to make the case for deep nuclear reductions and other forms of security cooperation as necessary for strategic stability. While different versions of strategic stability analysis did sometimes produce innovative proposals, constructive negotiations, and successful ratification campaigns in the past, this analytical framework has become more of a hindrance than a help. Treating arms control as a predominantly technical way to make deterrence more stable by changing force structure characteristics, military operations, relative numbers of weapons on either side, or total number of nuclear weapons gives short shrift to political factors, including the fundamental assumptions about world politics that inform different arms control logics, the quality of political relations among leading states, and the political processes that affect negotiation, ratification, and implementation. This article compares two logics for arms control as a means to enhance strategic stability, one developed by the Cambridge community in the 1960s and one used by the Reagan administration and its successors, with current perspectives on strategic stability in which flexibility and freedom of action are preferable to predictability and arms control. It also contrasts what the Barack Obama administration has tried to achieve through strategic stability dialogues with Russia and China with how they envision security cooperation. It then presents an approach developed during the Cold War by Hedley Bull for thinking about both the technical and the political dimensions of arms control, and suggests that the logic of Cooperative Security (which shares important features with Bull's approach) is a more appropriate and productive way to think about arms control in the twenty-first century than strategic stability analysis is.