New Results Concerning Probability Distributions with Increasing Generalized Failure Rates

The generalized failure rate of a continuous random variable has demonstrable importance in operations management. If the valuation distribution of a product has an increasing generalized failure rate (that is, the distribution is IGFR), then the associated revenue function is unimodal, and when the generalized failure rate is strictly increasing, the global maximum is uniquely specified. The assumption that the distribution is IGFR is thus useful and frequently held in recent pricing, revenue, and supply chain management literature. This note contributes to the IGFR literature in several ways. First, it investigates the prevalence of the IGFR property for the left and right truncations of valuation distributions. Second, we extend the IGFR notion to discrete distributions and contrast it with the continuous distribution case. The note also addresses two errors in the previous IGFR literature. Finally, for future reference, we analyze all common (continuous and discrete) distributions for the prevalence of the IGFR property, and derive and tabulate their generalized failure rates.

Childhood Adoption: Long-Term Effects in Adulthood

Clinicians and researchers have characterized early life experiences as permanent and stable influences on the personality and subsequent life experiences of an individual. Recent conceptualizations have suggested that personal and environmental factors influencing development are not deterministic. Multiple pathways into adulthood are possible. Adoption is one potential early life stressor that may illustrate the usefulness of such conceptualizations for assessing long-term effects in adulthood. Previous studies of adoption have characterized the effects of adoption into adolescence and young adulthood. The purpose of this study was to provide an initial assessment of the long-term impact of adoption. The participants were taken from the Swedish Adoption/Twin Study of Aging. From the original sample, we identified a subsample of 60 pairs of twins who were separated and reared apart, with one member being raised by a biological parent or parents and the other by an adoptive parent or parents with no biological relationship. A series of univariate and multivariate analyses were undertaken to assess the elements associated with being reared in either an adoptive home or the home of biological parent(s). The results suggest few significant effects of adoption on the adult adjustment of adoptees. In particular, the results reflect the important mediating role of childhood socioeconomic status, suggesting that the stress of adoption itself is mediated by the type of rearing environment provided by the adoption process.