Inequalities for linear combinations of gamma random variables

We study the behavior of the tail probabilities of weighted averages of certain independently and identically distributed random variables as the weights are varied. We show that the upper and lower tails are smallest when all the weights are equal. Our results apply to exponential, chi-squared, gamma, and Weibull random variables.     

Risk and final offer arbitration usage rates: Evidence from major league baseball

We use major league baseball data to examine risk and final-offer arbitration usage. Risk attitudes are proxied by the likelihood that FOA-generated salary increases place the player’s baseball employment at risk. Employment risk is inversely related to player quality. Our evidence suggests that higher-quality (low-risk) players are more likely to file for arbitration and seek an arbitrated settlement than lowerquality (high-risk) players. We thank Paul Burgess for helpful comments on an earlier version of this paper.     

WHY FAMILY THERAPY SHOULD GO BEYOND HOMEOSTASIS: A KUHNIAN REPLY TO ARIEL,CAREL AND TYANO

The thesis of “Beyond Homeostasis” is (a) that the discourse of family therapists unquestionably shows that family therapists have tended to see homeostasis as a trait of families; and (b) that such a view of homeostasis is inconsistent with the systemic paradigm. Therefore, family therapy should go beyond such an understanding of homeostasis. Ariel et al. may have failed to grasp this argument; they have certainly chosen to ignore it. Ariel et al. have provided a logical empiricist explication of the nonsystemic version of homeostasis which is portrayed in the discourse of family therapists. I still argue that family therapy should go beyond such an understanding of homeostasis.     

Bayes and empirical Bayes shrinkage estimation of regression coefficients

For a moderate or large number of regression coefficients, shrinkage estimates towards an overall mean are obtained by Bayes and empirical Bayes methods. For a special case, the Bayes and empirical Bayes shrinking weights are shown to be asymptotically equivalent as the amount of shrinkage goes to zero. Based on comparisons between Bayes and empirical Bayes solutions, a modification of the empirical Bayes shrinking weights designed to guard against unreasonable overshrinking is suggested. A numerical example is given.     

Equal Relationships: Fostering Growth for Clients and Counselors

Luthman, S. G., & Kirschenbaum, M. The Dynamic Family .
Stapleton, J., & Bright, R. Equal Marriage .     

An Insight Approach to Marital Therapy

The trend in marital therapy has traditionally been away from insight approaches and toward action-oriented methods, such as manipulating the couple system or teaching partners to negotiate. This paper presents a form of insight therapy based upon systems theory and suggests that this orientation has much to offer. The first part describes general categories of relationship problems with which a couples therapist must deal. The second part takes each of these problem types and suggests how a therapist with the present systems-interpretive approach might proceed. The goal is a shared understanding by partners of their marital system.