empirical distribution
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Risks ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 19
Author(s):  
Albert Pitarque ◽  
Montserrat Guillen

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.


2021 ◽  
Author(s):  
Boxiao Chen ◽  
David Simchi-Levi ◽  
Yining Wang ◽  
Yuan Zhou

We consider the periodic review dynamic pricing and inventory control problem with fixed ordering cost. Demand is random and price dependent, and unsatisfied demand is backlogged. With complete demand information, the celebrated [Formula: see text] policy is proved to be optimal, where s and S are the reorder point and order-up-to level for ordering strategy, and [Formula: see text], a function of on-hand inventory level, characterizes the pricing strategy. In this paper, we consider incomplete demand information and develop online learning algorithms whose average profit approaches that of the optimal [Formula: see text] with a tight [Formula: see text] regret rate. A number of salient features differentiate our work from the existing online learning researches in the operations management (OM) literature. First, computing the optimal [Formula: see text] policy requires solving a dynamic programming (DP) over multiple periods involving unknown quantities, which is different from the majority of learning problems in OM that only require solving single-period optimization questions. It is hence challenging to establish stability results through DP recursions, which we accomplish by proving uniform convergence of the profit-to-go function. The necessity of analyzing action-dependent state transition over multiple periods resembles the reinforcement learning question, considerably more difficult than existing bandit learning algorithms. Second, the pricing function [Formula: see text] is of infinite dimension, and approaching it is much more challenging than approaching a finite number of parameters as seen in existing researches. The demand-price relationship is estimated based on upper confidence bound, but the confidence interval cannot be explicitly calculated due to the complexity of the DP recursion. Finally, because of the multiperiod nature of [Formula: see text] policies the actual distribution of the randomness in demand plays an important role in determining the optimal pricing strategy [Formula: see text], which is unknown to the learner a priori. In this paper, the demand randomness is approximated by an empirical distribution constructed using dependent samples, and a novel Wasserstein metric-based argument is employed to prove convergence of the empirical distribution. This paper was accepted by J. George Shanthikumar, big data analytics.


2021 ◽  
Vol 12 ◽  
Author(s):  
Roberto Martin del Campo Vera ◽  
Edmond Jonckheere

In this paper, a new electromyographic phenomenon, referred to as Bursting Rate Variability (BRV), is reported. Not only does it manifest itself visually as a train of short periods of accrued surface electromyographic (sEMG) activity in the traces, but it has a deeper underpinning because the sEMG bursts are synchronous with wavelet packets in the D8 subband of the Daubechies 3 (db3) wavelet decomposition of the raw signal referred to as “D8 doublets”—which are absent during muscle relaxation. Moreover, the db3 wavelet decomposition reconstructs the entire sEMG bursts with two contiguous relatively high detail coefficients at level 8, suggesting a high incidence of two consecutive neuronal discharges. Most importantly, the timing between successive bursts shows some variability, hence the BRV acronym. Contrary to Heart Rate Variability (HRV), where the R-wave is easily identified, here, time-localization of the burst requires a statistical waveform matching between the “D8 doublet” and the burst in the raw sEMG signal. Furthermore, statistical fitting of the empirical distribution of return times shows a striking difference between control and quadriplegic subjects. Finally, the BRV rate appears to be within 60–88 bursts per minute on average among 9 human subjects, suggesting a possible connection between BRV and HRV.


Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3003
Author(s):  
Jurgita Arnastauskaitė ◽  
Tomas Ruzgas ◽  
Mindaugas Bražėnas

The testing of multivariate normality remains a significant scientific problem. Although it is being extensively researched, it is still unclear how to choose the best test based on the sample size, variance, covariance matrix and others. In order to contribute to this field, a new goodness of fit test for multivariate normality is introduced. This test is based on the mean absolute deviation of the empirical distribution density from the theoretical distribution density. A new test was compared with the most popular tests in terms of empirical power. The power of the tests was estimated for the selected alternative distributions and examined by the Monte Carlo modeling method for the chosen sample sizes and dimensions. Based on the modeling results, it can be concluded that a new test is one of the most powerful tests for checking multivariate normality, especially for smaller samples. In addition, the assumption of normality of two real data sets was checked.


2021 ◽  
Author(s):  
Ahmed A. Metwally ◽  
Tom Zhang ◽  
Si Wu ◽  
Ryan Kellogg ◽  
Wenyu Zhou ◽  
...  

Longitudinal studies increasingly collect rich 'omics' data sampled frequently over time and across large cohorts to capture dynamic health fluctuations and disease transitions. However, the generation of longitudinal omics data has preceded the development of analysis tools that can efficiently extract insights from such data. In particular, there is a need for statistical frameworks that can identify not only which omics features are differentially regulated between groups but also over what time intervals. Additionally, longitudinal omics data may have inconsistencies, including nonuniform sampling intervals, missing data points, subject dropout, and differing numbers of samples per subject. In this work, we developed a statistical method that provides robust identification of time intervals of temporal omics biomarkers. The proposed method is based on a semi-parametric approach, in which we use smoothing splines to model longitudinal data and infer significant time intervals of omics features based on an empirical distribution constructed through a permutation procedure. We benchmarked the proposed method on five simulated datasets with diverse temporal patterns, and the method showed specificity greater than 0.99 and sensitivity greater than 0.72. Applying the proposed method to the Integrative Personal Omics Profiling (iPOP) cohort revealed temporal patterns of amino acids, lipids, and hormone metabolites that are differentially regulated in male versus female subjects following a respiratory infection. In addition, we applied the longitudinal multi-omics dataset of pregnant women with and without preeclampsia, and the method identified potential lipid markers that are temporally significantly different between the two groups. We provide an open-source R package, OmicsLonDA (Omics Longitudinal Differential Analysis): https://bioconductor.org/packages/OmicsLonDA to enable widespread use.


2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Yixing Zhao ◽  
Rogemar Mamon ◽  
Heng Xiong

AbstractThis study considers the risk management of insurance policies in line with the implementation of the new International Financial Reporting Standards 17. It applies the paid-incurred chain method to model the future unpaid losses by combining the information channels of both the incurred claims and paid losses. We propose the recovery of the empirical distribution of the outstanding claims liabilities associated with a group of contracts via moment-based density approximation. We determine the risk measures and adjustments that are compliant with the new standard using the Monte–Carlo simulation method and approximated distributions. The historical data on the aggregate Ontario automobile insurance claims over a 15-year period are analyzed to examine the appropriateness and accuracy of our approach.


2021 ◽  
Vol 2094 (2) ◽  
pp. 022001
Author(s):  
B Kh Tazmeev ◽  
V V Tsybulevsky

Abstract High-speed visualization of the discharge with a liquid cathode, color image processing were performed. The area of cathode spots concentration was identified. Statistical characteristics of the distribution of cathode spots were obtained in order to determine the range in which the intensity code of the green color channel changes, the polygon function of the empirical distribution of the intensity code for the green color channel. The graphical dependence on the frequency of the cathode spot indication hit into the specified interval of the color intensity code was created.


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