Optimal upper bounds on expected kth record values from IGFR distributions

Statistical Inference Based on Upper Record Values

The goal of this thesis is to examine methods of statistical inference based on upper record values. This includes estimation of parameters based on samples of record values and prediction of future record values. We first define and discuss record times and record values and their distributions. Then we propose an efficient algorithm to generate random samples of record values. The algorithm, ...

Upper Bounds and Values For

Let r(G,H) be the smallest integer N such that for any 2-coloring (say, red and blue) of the edges of Kn, n > N there is either a red copy of G or a blue copy of H . Let Kn − K1,s be the complete graph on n vertices from which the edges of K1,s are dropped. In this note we present exact values for r(Km −K1,1,Kn −K1,s) and new upper bounds for r(Km,Kn−K1,s) in numerous cases. We also present som...

Bounds on Expectations of Record Range and Record Increment from Distributions with Bounded Support

In this paper, we consider the record statistics at the time when the nth record of any kind (either an upper or lower) is observed based on a sequence of independent random variables with identical continuous distributions of bounded support. We provide sharp upper bounds for expectations of record range and current upper record increment. We also present numerical evaluations of the so obtain...

Characterizations of Distributions by Expected Values of Lower Record Statistics with Spacing

Bounds on optimal values in stochastic scheduling

Consistent stochastic orders of processing times and objective functions yield optimal policies in many stochastic scheduling problems. When these orders fail to hold, however, finding optimal values may be difficult. In this paper, we show how to bound these values in general situations including problems with unreliable machines and tardiness-based objectives.