Interpolation of Quantile Regression to Estimate Driver’s Risk of Traffic Accident Based on Excess Speed

Quantile regression provides a way to estimate a driver’s risk of a traffic accident by means of predicting the percentile of observed distance driven above the legal speed limits over a one year time interval, conditional on some given characteristics such as total distance driven, age, gender, percent of urban zone driving and night time driving. This study proposes an approximation of quantile regression coefficients by interpolating only a few quantile levels, which can be chosen carefully from the unconditional empirical distribution function of the response. Choosing the levels before interpolation improves accuracy. This approximation method is convenient for real-time implementation of risky driving identification and provides a fast approximate calculation of a risk score. We illustrate our results with data on 9614 drivers observed over one year.

Nonparametric Estimation of Multivariate Extreme Value Copulas with Known and Unknown Marginal Distributions

The purpose of this paper is estimating the dependence function of multivariate extreme values copulas. Different nonparametric estimators are developed in the literature assuming that marginal distributions are known. However, this assumption is unrealistic in practice. To overcome the drawbacks of these estimators, we substituted the extreme value marginal distribution by the empirical distribution function. Monte Carlo experiments are carried out to compare the performance of the Pickands, Deheuvels, Hall-Tajvidi, Zhang and Gudendorf-Segers estimators. Empirical results showed that the empirical distribution function improved the estimators’ performance for different sample sizes.

Failure Extropy, Dynamic Failure Extropy and Their Weighted Versions

Extropy was introduced as a dual complement of the Shannon entropy. In this investigation, we consider failure extropy and its dynamic version. Various basic properties of these measures are presented. It is shown that the dynamic failure extropy characterizes the distribution function uniquely. We also consider weighted versions of these measures. Several virtues of the weighted measures are explored. Finally, nonparametric estimators are introduced based on the empirical distribution function.

An Asymptotic Test for Bimodality Using The Kullback–Leibler Divergence

Detecting bimodality of a frequency distribution is of considerable interest in several fields. Classical inferential methods for detecting bimodality focused in third and fourth moments through the kurtosis measure. Nonparametric approach-based asymptotic tests (DIPtest) for comparing the empirical distribution function with a unimodal one are also available. The latter point drives this paper, by considering a parametric approach using the bimodal skew-symmetric normal distribution. This general class captures bimodality, asymmetry and excess of kurtosis in data sets. The Kullback–Leibler divergence is considered to obtain the statistic’s test. Some comparisons with DIPtest, simulations, and the study of sea surface temperature data illustrate the usefulness of proposed methodology.

A Method for Solving Reliability of Route Travel Time

In order to obtain an effective method for solving route travel time reliability, this paper proposes an effective new method to calculate travel time reliability using an independent link travel time function. Based on several months of historical data, the results show that the Edgeworth expansion can better reflect travel time distribution law. In addition, travel time reliability can be calculated more conveniently by combining an approximate discretization algorithm and an empirical distribution function.

Control charts based on quantiles: New approaches

Contemporary development of Statistical quality control includes researches on different control charts, which could be easily implemented in production processes due to facilities offered by computers. New control charts give more information about production processes than the conventional ones, that's why there is a lot of investigation in this area of applied statistics. In this paper, we shall explain some new ideas concerning the construction of control charts based on quantiles, empirical distribution function and p-value.

Empirical distribution function as a tool in quality control

In this paper, we are introducing two new methods for Quality Control. Those methods rely on using the Empirical distribution function of a given sample (or several samples). The first method we use for one sample, i.e. we can determine if each given sample is adequate. We use the second method to determine whether several samples are "in control" or not. For the sample to be "in control" state, the normal distribution is required.