The Generalised Plug-in Algorithm for the Diffeomorphism Kernel Estimate

The optimal value of the smoothing parameter of the Kernel estimator can be obtained by the well known Plug-in algorithm. The optimality is realised in the sense of Mean Integrated Square Error (MISE). In this paper, we propose to generalise this algorithm to the case of the difficult problem of the estimation of a distribution which has a bounded support. The proposed algorithm consists in searching the optimal smoothing parameter by iterations from the expression of MISE of the kernel-diffeomorphism estimator. By some simulations applied to some distribution having a support bounded and semi bounded, we show that the support of the pdf estimator respects the one of the theoretical distribution. We also prove that the proposed method minimizes the Gibbs phenomenon.

How should we investigate variation in the relation between social media and well-being?

The study of the relation between social media use and well-being is at a critical junction. Many researchers find small to no associations, yet policymakers and public stakeholders keep asking for more evidence. One way the field is reacting is by inspecting the variation around average relations – with the goal of describing individual social media users. Here, we argue that such an approach risks losing sight of the most important outcomes of a quantitative social science: estimates of the average relation in a large group. Our analysis begins by describing how the field got to this point. Then, we explain the problems of the current approach of studying variation. Next, we propose a principled approach to quantify, interpret, and explain variation in average relations: (1) conducting model comparisons, (2) defining a region of practical equivalence and testing the theoretical distribution of relations against that region, (3) defining a smallest effect size of interest and comparing it against the theoretical distribution. We close with recommendations to either study moderators as systematic factors that explain variation or to conduct N = 1 studies and qualitative research.

Identification of Statistical Distribution Type by Sample Data

The present paper provides a full description of a software implementation of a system for statistical distributions. Such a system is almost indispensable in many simulation applications where the factors incorporated adhere to a specific non-normal distribution. The realization is developed as a software library that can be integrated in different other applications. There is also the possibility for additional theoretical distribution types to be added.

Modeling Crossing Random Seas by Fully Non-Linear Numerical Simulations

Bimodal spectrum wave conditions, known as crossing seas, can produce extreme waves which are hostile to humans during oceanic activities. This study reports some new findings of the probability of extreme waves in deep crossing random seas in response to the variation of spectral bandwidth through fully non-linear numerical simulations. Two issues are addressed, namely (i) the impacts of the spectral bandwidth on the changes of extreme wave statistics, i.e., the kurtosis and crest exceedance probability, and (ii) the suitability of theoretical distribution models for accurately describing the wave crest height exceedance probability in crossing seas. The numerical results obtained by simulating a large number of crossing sea conditions on large spatial-temporal scale with a variety of spectral bandwidth indicate that the kurtosis and crest height exceedance probability will be enhanced when the bandwidth of each wave train becomes narrower, suggesting a higher probability of encountering extreme waves in narrowband crossing seas. Meanwhile, a novel empirical formula is suggested to predict the kurtosis in crossing seas provided the bandwidth is known in advance. In addition, the Rayleigh and second-order Tayfun distribution underestimate the crest height exceedance probability, while the third-order Tayfun distribution only yields satisfactory predictions for cases with relatively broader bandwidth regarding the wave conditions considered in this study. For crossing seas with narrower bandwidth, all the theoretical distribution models failed to accurately describe the crest height exceedance probability of extreme waves.

Statistical Calculations

This chapter presents statistical commands and its applications to various problems of the mechanics and tribology (M&T). Descriptive statistics, data statistics tool, specialized statistical graphs, probability distributions, and hypothesis tests are discussed. The solutions of various applied problems are given. In particular, surface roughness indices are calculated by the measured data using the descriptive statistics command; the histogram generated by a runout data are matched with the theoretical distribution; capability plot generation is shown by the data for the piston ring gaps; friction torques for two different oil additives are compared using a hypothesis test.

Statistical analysis of the vehicles main dimensions variability on public roads

The aim of the study is to obtain the parameters of vehicle size variability and evaluate the convergence of empirical data with the modeling results using distribution functions. The main results of the study consist in obtaining statistical parameters that characterize the variability of vehicle sizes, and testing hypotheses about whether the empirical distribution belongs to one of the theoretical distribution functions. The significance of the obtained results lies in the possibility of using the most suitable theoretical functions of probability distributions of random variables that characterize the variability of vehicle sizes in algorithms for estimating the resource parameters of steel spans of road bridges.

Appropriate Distribution of Cost Inefficiency Estimates as Predictor of Financial Instability

The study develops a hypothesis validation process to test whether estimated cost inefficiency fits the theoretical distribution of the estimate of inefficiency, given the initial assumption of a half normal distribution for the inefficiency term in the stochastic frontier model. The application of this methodology to a sample of Spanish banks in the period 2002-2007 allows us to observe the evolution of the distributions of estimated cost inefficiency. The results confirm for the existence of a relationship between estimated cost inefficiency and the financial situation of these entities. In fact, an increase in the probability of higher levels of inefficiency is observed the period of study, coinciding with the beginning of financial instability in the Spanish banking system.

The L-moment based regional approach to curve numbers for Slovak and Polish Carpathian catchments

The main objective of the paper was to propose and evaluate the performance of a regional approach to estimate CN values and to test the impact of different initial abstraction ratios. The curve number (CN) was analyzed for five Slovak and five Polish catchments situated in the Carpathian Mountains. The L-moment based method of Hosking and Wallis and the ANOVA test were combined to delineate the area in two homogenous regions of catchments with similar CN values. The optimization condition enabled the choice of the initial abstraction ratio, which provided the smallest discrepancy between the tabulated and estimated CNs and the antecedent runoff conditions. The homogeneity in the CN within the regions of four Slovak and four Polish catchments was revealed. Finally, the regional CN was proposed to be at the 50% quantile of the regional theoretical distribution function estimated from all the CNs in the region.The approach is applied in a group of Slovak and Polish catchments with physiographic conditions representative for the Carpathian region. The main benefit of introducing a common regional CN is the opportunity to apply this procedure in catchments of similar soil-physiographic characteristics and to verify the existing tabulated CN. The paper could give rise to an alternative way of estimating the CN values in forested catchments and catchments with a lack of data or without observations.