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A Probability Model For Strategic Bidding On The Price Is Right, Paul H. Kvam
A Probability Model For Strategic Bidding On The Price Is Right, Paul H. Kvam
Department of Math & Statistics Faculty Publications
The TV game show “The Price is Right” features a bidding auction called “Contestants’ Row” that rewards the player (out of 4) who bids closest to an item’s value, without overbidding. This paper considers ways in which players can maximize a winning probability based on the player's bidding order. We consider marginal strategies in which players assume opponents are bidding individually perceived values of the merchandise. Based on preceding bids of others, players have information available to create strategies. We consider conditional strategies in which players adjust bids knowing other players are using strategies. The last bidder has a large …
Nonparametric Estimation Of A Distribution Subject To A Stochastic Precedence Constraint, Miguel A. Arcones, Paul H. Kvam, Francisco J. Samaniego
Nonparametric Estimation Of A Distribution Subject To A Stochastic Precedence Constraint, Miguel A. Arcones, Paul H. Kvam, Francisco J. Samaniego
Department of Math & Statistics Faculty Publications
For any two random variables X and Y with distributions F and G defined on [0,∞), X is said to stochastically precede Y if P(X≤Y) ≥ 1/2. For independent X and Y, stochastic precedence (denoted by X≤spY) is equivalent to E[G(X–)] ≤ 1/2. The applicability of stochastic precedence in various statistical contexts, including reliability modeling, tests for distributional equality versus various alternatives, and the relative performance of comparable tolerance bounds, is discussed. The problem of estimating the underlying distribution(s) of experimental data under the assumption that they obey a …
Ranked Set Sampling From Location-Scale Families Of Symmetric Distributions, Ram C. Tiwari, Paul H. Kvam
Ranked Set Sampling From Location-Scale Families Of Symmetric Distributions, Ram C. Tiwari, Paul H. Kvam
Department of Math & Statistics Faculty Publications
Statistical inference based on ranked set sampling has primarily been motivated by nonparametric problems. However, the sampling procedure can provide an improved estimator of the population mean when the population is partially known. In this article, we consider estimation of the population mean and variance for the location-scale families of distributions. We derive and compare different unbiased estimators of these parameters based on independent replications of a ranked set sample of size n. Large sample properties, along with asymptotic relative efficiencies, help identify which estimators are best suited for different location-scale distributions.
Fisher Information In Weighted Distributions, Satish Iyengar, Paul H. Kvam, Harshinder Singh
Fisher Information In Weighted Distributions, Satish Iyengar, Paul H. Kvam, Harshinder Singh
Department of Math & Statistics Faculty Publications
Standard inference procedures assume a random sample from a population with density fμ(x) for estimating the parameter μ. However, there are many applications in which the available data are a biased sample instead. Fisher modeled biased sampling using a weight function w(x) ¸ 0, and constructed a weighted distribution with a density fμw(x) that is proportional to w(x)fμ(x). In this paper, we assume that fμ(x) belongs to an exponential family, and study the Fisher information about μ in observations obtained from some commonly arising weighted distributions: (i) the kth order …