Edge Estimation in the Population of a Binary Tree Using Node-Sampling

Suppose a finite population of several vertices, each connected to single or multiple edges. This constitutes a structure of graphical population of vertices and edges. As a special case, the graphical population like a binary tree having only two child vertices associated to parent vertex is taken into consideration. The entire binary tree is divided into two sub-graphs such as a group of left-nodes and a group of right-nodes. This paper takes into account a mixture of graph structured and population sampling theory together and presents a methodology for mean-edge-length estimation of left sub-graph using right edge sub-graph as an auxiliary source of information. A node-sampling procedure is developed for this purpose and a class of estimators is proposed containing several good estimators. Mathematical conditions for minimum bias and optimum mean squared error of the class are derived and theoretical results are numerically supported with a test of 99% confidence intervals. It is shown that suggested class has a sub-class of optimum estimators, and sample-based estimates are closer to the true value of the population parameter.     

Calculation of multidimensional stable densities

Stable random variables are used in economics, engineering, hydrology and physics to model situations where the underlying distributions are heavy tailed. Stable densities do not generally have explicit formula, even in one variable. This paper describes the steps necessary to calculate multivariate stable densities by numerically inverting the characteristic function. We give a program tocalculate two dimensional stable densites that uses a recent two dimensional adaptive quadratureroutine. Graphs of families of such densities are given for a range of values of a and various spectral measures     

Children's Interpretations of Ambiguous Provocation From Their Siblings: Comparisons With Peers and Links to Relationship Quality

This study investigated how six‐ to eight‐year‐old children interpret ambiguous provocation from their siblings. In particular, we examined how children's attributions of their siblings' intent (1) differed from those for their peers, (2) varied as a function of the structural features of the sibling relationship, and (3) were associated with the affective qualities of the sibling relationship. A total of 121 children were presented with ambiguous provocation scenarios in which three groups of agemates were described as the perpetrators of harm (siblings, friends, and disliked peers). Scenarios were designed to assess children's attributions of hostile, instrumental, and accidental intent. Children attributed more hostile intent to disliked peers than to siblings and less hostile intent to friends than to siblings. Accidental and instrumental intent attributions were equally likely for friends and siblings but less common for disliked peers. Children attributed more hostile intent to older siblings, and more instrumental intent to laterborn siblings who were chronologically younger. Children's attributions of siblings' intent were related to both parents' and children's reports of the affective features of siblings' interactions. Results provide new insight into how children's construals of others' actions are grounded in the unique features of their relationships with particular interaction partners.