Recursive procedures for multiple decisions: finite time memory and stepwise maximum likelihood procedure

A version of the multiple decsion problem is studied in which the procedure is based only on the current observation and the previous decision. A necessary and sufficient condition for inconsistency of the stepwise maximum likelihood procedure is shown to be the boundedness of the likelihood ratios. In the case of consistency the (typically slow) rate of convergence to zero of the error probabilities is determined.     

Estimation and Extrapolation of Tumor Probabilities from a Mouse Bioassay with Survival/Sacrifice Components

A nonparametric estimator of the probability distribution of time-to-tumor is incorporated into an algorithm for calculating linearly extrapolated dosage limits from an animal carcino-genesis bioassay. The procedure is illustrated with tumor data from a mouse bioassay with 2-acetylaminofluorene. Extrapolated dosage limits for an excess risk of 10^-6 differ by only a factor of 2 across the six replicates of the experiment.     

Some computational problems related to multinomial trials

Efficient numerical algorithms are developed to evaluate several probabilities related to multinomial trials.In the first part of the paper, the probability distribution of the number of trials until the alternatives j, j = 1,… m, have occurred at least i_j times is computed. The multinomial trials involve the m alternatives l,…, m, with positive probabilities P_l-P_m of occurrence. In the second part, several aspects of a multinomial subset selection problem, discussed by S. S. Gupta and K. Nagel, are investigated.     

Inference for a Simple Step-Stress Model with Type-I Censoring and Lognormally Distributed Lifetimes

Accelerated life-testing (ALT) is a very useful technique for examining the reliability of highly reliable products. It allows the experimenter to obtain failure data more quickly at increased stress levels than under normal operating conditions. A step-stress model is one special class of ALT, and in this article we consider a simple step-stress model under the cumulative exposure model with lognormally distributed lifetimes in the presence of Type-I censoring. We then discuss inferential methods for the unknown parameters of the model by the maximum likelihood estimation method. Some numerical methods, such as the Newton–Raphson and quasi-Newton methods, are discussed for solving the corresponding non-linear likelihood equations. Next, we discuss the construction of confidence intervals for the unknown parameters based on (i) the asymptotic normality of the maximum likelihood estimators (MLEs), and (ii) parametric bootstrap resampling technique. A Monte Carlo simulation study is carried out to examine the performance of these methods of inference. Finally, a numerical example is presented in order to illustrate all the methods of inference developed here.     

Nonparametric Predictive Inference for Ordinal Data

Nonparametric predictive inference (NPI) is a powerful frequentist statistical framework based only on an exchangeability assumption for future and past observations, made possible by the use of lower and upper probabilities. In this article, NPI is presented for ordinal data, which are categorical data with an ordering of the categories. The method uses a latent variable representation of the observations and categories on the real line. Lower and upper probabilities for events involving the next observation are presented, and briefly compared to NPI for non ordered categorical data. As application, the comparison of multiple groups of ordinal data is presented.     

Some Results on Modeling Biological Sequences and Web Navigation with a Semi Markov Chain

In the article, the entrance probabilities and the probability distribution of the number of transitions to a state are studied to provide some answers to questions related to state occupancies for the semi Markov model. Biological sequences and Web navigation are two cases that initially seem to be different but to a certain extent they do have similarities. Two main aspects of word occurrences in biological sequences are: (a) where do they occur and (b) how many times do they occur. In Web navigation the similar questions are (a) when a node is visited and (b) how many times a node is visited. So, the theoretical results of this study are applied to model these two cases and derive distributions of word location or node occurrence and frequency of occurrences. Rewards/costs are included in the Web navigation model and analytic forms for the means, variances, and moments of total interval rewards/costs are provided.     

Operating Characteristics of a Subset Selection Procedure Applied to a Hybrid Randomized Response Model

The operating characteristics (OCs) of a subset ranking and selection procedure are derived for the hybrid randomized response model developed by Jia and McDonald (2009 Jia, F., McDonald, G. (2009). Analyzing hybrid randomized response data with a binomial selection procedure. Commun. Statist. Theor. Meth. 38:784807.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). The OCs include the probability of a correct P(CS), the individual selection probability γ_i, and the expected subset size E(S), under the slippage configuration or the equi-spaced configuration. An example comparing failure rates of contraceptive methods is used to illustrate the use of these new results.     

Equilibrium probabilities for a production-inventory system maintained by a control-limit policy

Abstract

In this paper we consider a manufacturing system in which an input generator supplies at a constant rate a buffer with a raw material and a production unit pulls the raw material from the buffer at a stochastic rate. We consider specific control-limit policies for the maintenance of the production unit. We show that the equilibrium probabilities of the system can be computed exactly when the production unit after a maintenance remains idle until the buffer is filled up.     

Asymptotic expansions in non-linear renewal theory

We obtain first order asymptotic expansions for the distribution of the excess of a standard normal random walk over a curved boundary and the error probabilities of some repeated significance tests. The key step in the analysis is an asymptotic expansion for the conditional probability that the random walk has not crossed the boundary before the N step, given that it is near the boundary after the n^th step.     

An asymptotic expression for cumulative sum of probabilities of the hermite distribution

An asymptotic approximation of cumulative sum F(s) of probabilities of the Hermite distribution (Kemp C. D. and Kemp A. W. (1965)) and an asymptotic approximation of individual Hemite Probability P_s are given for large s.