Faster algorithm to find anti-risk path between two nodes of an undirected graph

For a weighted 2-edge connected graph G=(V,E), we are to find a “minimum risk path” from source s to destination t. This is a shortest s?t path under the assumption that at most one edge on the path may be blocked. The fact that the edge is blocked is known only when we reach a site adjacent to the blocked edge. If n and m are the number of nodes and edges of G, then we show that this problem can be solved in O(n ²) time using only simple data structures. This is an improvement over the previous O(mn+n ²logn) time algorithm. Moreover, with use of more complicated data structures like Fibonacci Heaps and transmuters the time can be further reduced to O(m+nlogn).     

Maximum cardinality neighbourly sets in quadrilateral free graphs

Neighbourly set of a graph is a subset of edges which either share an end point or are joined by an edge of that graph. The maximum cardinality neighbourly set problem is known to be NP-complete for general graphs. Mahdian (Discret Appl Math 118:239–248, 2002) proved that it is in polynomial time for quadrilateral-free graphs and proposed an \(O(n^{11})\) algorithm for the same, here n is the number of vertices in the graph, (along with a note that by a straightforward but lengthy argument it can be proved to be solvable in \(O(n^5)\) running time). In this paper we propose an \(O(n^2)\) time algorithm for finding a maximum cardinality neighbourly set in a quadrilateral-free graph.     

Exploring Home Sharing for Elders

Research suggests that third party-arranged home sharing (“TPAHS”) enables elders to remain at home in advanced age by connecting elder home owners with suitable live-in “matches.” TPAHS potentially saves elders, their families, and Medicaid budgets millions of a dollars per year in avoided and postponed nursing home costs. In interviews with elder TPAHS participants of one TPAHS program, we found that similarity in values, ability to utilize the TPAHS organization's guidance, and, when relevant, familiarity with their matches' mental health challenges, correlated with said participants' satisfaction with their matches while a lack of these qualities correlated with match dissatisfaction. With these findings in mind, we suggest strategies TPAHS organizations can use to best serve the elderly TPAHS participants who may benefit from intensified match support but may not seek it.     

Inference from the Exponentiated Weibull Model with Applications to Real Data

In this paper, a novel Bayesian framework is used to derive the posterior density function, predictive density for a single future response, a bivariate future response, and several future responses from the exponentiated Weibull model (EWM). We study three related types of models, the exponentiated exponential, exponentiated Weibull, and beta generalized exponential, which are all utilized to determine the goodness of fit of two real data sets. The statistical analysis indicates that the EWM best fits both data sets. We determine the predictive means, standard deviations, highest predictive density intervals, and the shape characteristics for a single future response. We also consider a new parameterization method to determine the posterior kernel densities for the parameters. The summary results of the parameters are calculated by using the Markov chain Monte Carlo method.     

From Ordinary to Shrinkage Square-Root Estimators

Consider a skewed population. Suppose an intelligent guess could be made about an interval that contains the population mean. There may exist biased estimators with smaller mean squared error than the arithmetic mean within such an interval. This article indicates when it is advisable to shrink the arithmetic mean towards a guessed interval using root estimators. The goal is to obtain an estimator that is better near the average of natural origins. An estimator proposed. This estimator contains the Thompson (1968 Thompson , J. R. ( 1968 ). Accuracy borrowing in the estimation of the mean by shrinkage towards an interval . J. Amer. Statist. Assoc. 63 : 953 – 963 . [CSA] [CROSSREF] [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) ordinary shrinkage estimator, the Jenkins et al. (1973 Jenkins , O. C. , Ringer , L. J. , Hartley , H. O. ( 1973 ). Root estimators . J Amer. Statist. Assoc. 68 : 414 – 419 . [CSA] [CROSSREF] [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) square-root estimator, and the arithmetic sample mean as special cases. The bias and the mean squared error of the proposed more general estimator is compared with the three special cases. Shrinkage coefficients that yield minimum mean squared error estimators are obtained. The proposed estimator is considerably more efficient than the three special cases. This remains true for highly skewed populations. The merits of the proposed shrinkage square-root estimator are supported by the results of numerical and simulation studies.     

Understanding Gender and Power Dynamics Within the Family: A Qualitative Study of Nepali Women's Experience

Among the Maori of New Zealand, Aboriginals of Australia, and other Indigenous peoples, family dynamics strongly influence the ways that issues emerge in counseling. This study explores aspects of gender and power within the context of birth practices in rural Nepal. In‐depth interviews were conducted with 15 postpartum women, as well as family members, to collect narratives of birthing experiences that highlight issues of oppression, marginalisation, and power struggles. Implications for multicultural and social justice awareness in family therapy are discussed, especially with regard to the subtle, disguised ways that power operates behind the scenes, often sabotaging efforts by health and mental health professionals to bemost helpful.     

Estimation of coefficient of dispersion using auxiliary information

In this note, we consider the problem of estimation of coefficient of dispersion of a study variable by making use of known value of the coefficient of dispersion of an auxiliary variable. We propose ratio and regression-type estimators. We derive expressions of bias and variance of the proposed estimators to the first order of approximation. The relative efficiencies of the ratio and regression-type estimators with respect to the naïve estimator are investigated through a simulation study.     

On the inadmssibelity of ridge estimator in a linear model

The necessary and sufficient conditions for the inadmissibility of the ridge regression is discussed under two different criteria, namely, average loss and Pitman nearness. Although the two criteria are very different, same conclusions are obtained. The loss functions considered in this article are th likelihood loss function and the Mahalanobis loss function. The two loss functions are motivated from the point of view of classification of two normal populations. Under the Mahalanobis loss it is demonstrated that the ridge regression is always inadmissible as long as the errors are assumed to be symmetrically distributed about the origin.     

Risk averse demand selection with all-or-nothing orders

Consider a firm that operates in consecutive single selling seasons, delivering its products across several markets with unique revenue and uncertain demands in each market. Using a profit maximization approach based on a newsvendor-type model, the firm may still incur several losses across consecutive periods in the short run. Risk analysis with demand selection has been modeled where customer/market demands follow a normal distribution. Often a firm faces a set of potential unconfirmed orders, where each order will either come in at a predefined level or it will not come in at all. In this paper, we consider these all-or-nothing (AON) demands and provide insights into their effect on expected profit and the frequency of extremely costly procurement policies. Instead of solely identifying the market/demand set and procurement quantity that maximizes expected profit, we use a conditional value-at-risk approach that allows a decision maker to control the number of profitable but risky demands to consider in the overall procurement policy. This approach is compared against an expected profit objective, and several managerial insights are provided.