The exponentiated-log-logistic geometric distribution: Dual activation

ABSTRACT

The log-logistic distribution is commonly used to model lifetime data. We propose a wider distribution, named the exponentiated log-logistic geometric distribution, based on a double activation approach. We obtain the quantile function, ordinary moments, and generating function. The method of maximum likelihood is used to estimate the model parameters. We propose a new extended regression model based on the logarithm of the exponentiated log-logistic geometric distribution. This regression model can be very useful in the analysis of real data and could provide better fits than other special regression models. The potentiality of the new models is illustrated by means of two applications to real lifetime data sets.     

Comparison of Four Bootstrap‐Based Interval Estimators of Species Occupancy and Detection Probabilities

Site occupancy, as estimated by the probability of presence, is used for monitoring species populations. However, the detection of species at individual sites is often subject to errors. In order to accurately estimate occupancy we must simultaneously account for imperfect detectability by estimating the probability of detection. The problem with estimating occupancy arises from not knowing whether a nondetection occurred at an occupied site due to imperfect detectability (sampling zeros), or the nondetection resulting from an unoccupied site (fixed zeros). We evaluated the performance of the basic, normal approximation, studentised and percentile methods for approximating confidence limits for occupancy and detection of species. Using coverage and average interval width, we demonstrated that the studentised estimator was generally superior to the others, except when a small sample of sites are selected. Under this circumstance and when calculating limits for detection, no estimator produced reliable results. The experimental factors we considered include: (i) number of sites; (ii) number of survey occasions; (iii) probabilities of presence (occupancy) and detection; and (iv) overdispersion in the capture matrix. Similar conclusions were reached both for the simulated studies and a case study. Overall, estimation near the boundaries of the probability of occupancy and detectability was difficult.     

Mother–Adolescent Conflict: Stability,Change, and Relations with Externalizing and Internalizing Behavior Problems

Stability and change in mother–adolescent conflict reactions (CRs) and the prediction of CRs from adolescents' earlier behavior problems (and vice versa) were examined with 131 mothers and their adolescents (63 boys). Dyads engaged in a 6‐min conflict discussion twice, 2 years apart [M age was 13 at Time 1 (T1)]. Non‐verbal expressive and verbal CRs during the conflict discussion were coded. Mothers, fathers, and teachers reported on adolescents' problem behaviors. There was inter‐individual (rank‐order) stability for adolescents' CRs whereas mothers' reactions were less stable. Mean levels of mothers' negativity, anger, and positive reactions and adolescents' negativity declined with time. Mothers’ CRs, more often than adolescents’ CRs, predicted and were predicted by adolescents’ problem behaviors in zero‐order correlations. In structural equation models with the stability of the constructs accounted for, adolescents' externalizing problems at T1 predicted higher maternal anger at Time 2 (T2). Mothers' anger and positive CRs at T1 predicted fewer T2 adolescents' internalizing problems. Stability and change in CRs are discussed.