We study a class of optimal allocation problems, including the well-known Bomber Problem, with the following common probabilistic structure. An aircraft equipped with an amount x of ammunition is intercepted by enemy airplanes arriving according to a homogenous Poisson process over a fixed time...

A problem of optimally allocating partially effective ammunition x to be used on randomly arriving enemies in order to maximize an aircraft's probability of surviving for time t, known as the Bomber Problem, was first posed by Klinger and Brown (1968). They conjectured a set of apparently...

The inequality conjectured by van den Berg and Kesten in [9], and proved by Reimer in [6], states that for A and B events on S, a product of finitely many finite sets, and P any product measure on S,P(AÊB) <FONT FACE="Symbol">£</FONT> P(A)P(B), where AÊB are the elementary events which lie in both A and B for `disjoint...</font>

We consider a permutation method for testing whether observations given in their natural pairing exhibit an unusual level of similarity in situations where any two observations may be similar at some unknown baseline level. Under a null hypothesis where there is no distinguished pairing of the...

In the context of survival analysis, we define a covariate X as protective (detrimental) for the failure time T if the conditional distribution of [T | X = x] is stochastically increasing (decreasing) as a function of x. In the presence of another covariate Y, there exist situations where [T | X...

Based on a model introduced by Kaminsky, Luks, and Nelson (1984), we consider a zero-sum allocation game called the Gladiator Game, where two teams of gladiators engage in a sequence of one-to-one fights in which the probability of winning is a function of the gladiators' strengths. Each team's...

Let X_n,…,X₁ be i.i.d. random variables with distribution function F and finite expectation. A statistician, knowing F, observes the X values sequentially and is given two chances to choose X's using stopping rules. The statistician's goal is to select a value of X as large as possible. Let V_n²...

Asymptotic results for the problem of optimal two choice stopping on an n element long i.i.d. sequence X<SUB>n</SUB>, . . . ,X<SUB>1</SUB> have previously been obtained for two of the three domains of attraction. An asymptotic result is proved for the exponential distribution, a representative from the remaining,...</sub></sub>

Let Xn, . . . ,X1 be i.i.d. random variables with distribution function F. A statistician, knowing F, observes the X values sequentially and is given two chances to choose X’s using stopping rules. The statistician’s goal is to stop at a value of X as small as possible. Let V^2 equal the...