Goodness--of--Fit Tests Based on the Min--Characteristic Function

We propose tests of fit for classes of distributions that include the Weibull, the Pareto and the Fr\'echet, distributions. The new tests employ the novel tool of the min--characteristic function and are based on an L2--type weighted distance between this function and its empirical counterpart applied on suitably standardized data. If data--standardization is performed using the MLE of the distributional parameters then the method reduces to testing for the standard member of the family, with parameter values known and set equal to one. We investigate asymptotic properties of the tests, while a Monte Carlo study is presented that includes the new procedure as well as competitors for the purpose of specification testing with three extreme value distributions. The new tests are also applied on a few real--data sets

Una generalización de la métrica de Hausdorff sobre C(Rn)

En este trabajo hacemos una extensión de la métrica de Hausdorff  sobre C(Rn), el espacio de todos los conjuntos difusos cerrados en Rn, obteniendo una familia de métricas Df . Estudiamos algunas propiedades topológicas del espacio métrico C(Rn),Df.  &nbsp

Evaluation of appendicitis risk prediction models in adults with suspected appendicitis

Background Appendicitis is the most common general surgical emergency worldwide, but its diagnosis remains challenging. The aim of this study was to determine whether existing risk prediction models can reliably identify patients presenting to hospital in the UK with acute right iliac fossa (RIF) pain who are at low risk of appendicitis. Methods A systematic search was completed to identify all existing appendicitis risk prediction models. Models were validated using UK data from an international prospective cohort study that captured consecutive patients aged 16–45 years presenting to hospital with acute RIF in March to June 2017. The main outcome was best achievable model specificity (proportion of patients who did not have appendicitis correctly classified as low risk) whilst maintaining a failure rate below 5 per cent (proportion of patients identified as low risk who actually had appendicitis). Results Some 5345 patients across 154 UK hospitals were identified, of which two‐thirds (3613 of 5345, 67·6 per cent) were women. Women were more than twice as likely to undergo surgery with removal of a histologically normal appendix (272 of 964, 28·2 per cent) than men (120 of 993, 12·1 per cent) (relative risk 2·33, 95 per cent c.i. 1·92 to 2·84; P < 0·001). Of 15 validated risk prediction models, the Adult Appendicitis Score performed best (cut‐off score 8 or less, specificity 63·1 per cent, failure rate 3·7 per cent). The Appendicitis Inflammatory Response Score performed best for men (cut‐off score 2 or less, specificity 24·7 per cent, failure rate 2·4 per cent). Conclusion Women in the UK had a disproportionate risk of admission without surgical intervention and had high rates of normal appendicectomy. Risk prediction models to support shared decision‐making by identifying adults in the UK at low risk of appendicitis were identified

A bootstrap test for the expectation of fuzzy random

variable

Bootstrapping statistical functionals

A modified bootstrap procedure is proposed. It is based on the outlier bootstrap sample concept introduced by Muñoz-García et al. (1997). The consistency of the modified bootstrap distribution estimator and of the modified bootstrap variance estimator is established for Féchet differentiable statistical functionals. The modified bootstrap variance estimator requires less stringent conditions for its consistency than the ordinary bootstrap variance estimator.Bootstrap Outlier bootstrap sample Distribution estimation Variance estimation Fréchet differentiability Consistency

A homogeneity test for bivariate random variables

Homogeneity, Bivariate populations, Empirical characteristic function, Quadratic Powell–Sabin splines, Quadratic Taylor approximation, Bootstrap,