Record values and the geometric distribution

Suppose {X_n, n≥1} is a sequence of independent and identically distributed discrete random variables having the common distribution function F(x). The exact distribution of the n-th record value is given under the assumption that F(x) has the geometric distribution. Various properties of the record values and some new characterizations of the geometric distribution are presented.     

Bayesian break-point forecasting in parallel time series,with application to university admissions

A regular supply of applicants to Queen's University in Kingston, Ontario is provided by 65 high schools. Each high school can be characterized by a series of grading standards which change from year to year. To aid admissions decisions, it is desirable to forecast the current year's grading standards for all 65 high schools using grading standards estimated from past year's data. We develop and apply a Bayesian break-point time-series model that generates forecasts which involve smoothing across time for each school and smoothing across schools. “Break point” refers to a point in time which divides the past into the “old past” and the “recent past” where the yearly observations in the recent past are exchangeable with the observations in the year to be forecast. We show that this model works fairly well when applied to 11 years of Queen's University data. The model can be applied to other data sets with the parallel time-series structure and short history, and can be extended in several ways to more complicated structures.     

Performance models for unreliable flexible manufacturing systems

This paper deals with the analysis and application of queueing models for single and multi stage flexible manufacturing systems that are subject to resource failure. Exact results are derived for the single stage queueing system. Two approximations are presneted for the multi stage queueing system as a closed network. We validate the approximations by comparing their performance estimates against the exact global balance solution.     

Symbiotic mothers and infantilized only children: A subtype of single-parent family

One single-parent family pattern is the enmeshed mother/onlychild dyad. Women marry to have children, and then divorce, while mother and child live out the reciprocally gratifying symbiotic period. When these mothers hamper offspring moves toward separation-individuation, post-divorce difficulties bring them to treatment. These difficulties are distinct from those found in other single-parent families. Intervention can move mother and child from the prolonged symbiosis. Treatment stresses modification of low maternal selfesteem, and correction of pathogenic maternal behavior. Re-introduction of the father to the system can also free both mother and child for further growth.