Strong Approximation of Quantile Function for Strong Mixing and Censored Processes

2005 ◽  
Vol 34 (7) ◽  
pp. 1449-1459 ◽  
Author(s):  
Elias Ould-Saïd ◽  
Ourida Sadki
Keyword(s):  
Strong Approximation ◽  
Quantile Function ◽  
Strong Mixing

An alternative distribution to Lindley and Power Lindley distributions with characterizations, different estimation methods and data applications

2020 ◽  
Vol 70 (4) ◽  
pp. 953-978
Author(s):  
Mustafa Ç. Korkmaz ◽  
G. G. Hamedani
Keyword(s):  
Hazard Function ◽  
Mixture Distribution ◽  
Real Data ◽  
Quantile Function ◽  
Estimation Methods ◽  
Data Sets ◽  
Unknown Parameters ◽  
Lorenz Curves ◽  
Proposed Model ◽  
New Distribution

AbstractThis paper proposes a new extended Lindley distribution, which has a more flexible density and hazard rate shapes than the Lindley and Power Lindley distributions, based on the mixture distribution structure in order to model with new distribution characteristics real data phenomena. Its some distributional properties such as the shapes, moments, quantile function, Bonferonni and Lorenz curves, mean deviations and order statistics have been obtained. Characterizations based on two truncated moments, conditional expectation as well as in terms of the hazard function are presented. Different estimation procedures have been employed to estimate the unknown parameters and their performances are compared via Monte Carlo simulations. The flexibility and importance of the proposed model are illustrated by two real data sets.

scholarly journals High-Dimensional Spatial Quantile Function-on-Scalar Regression

2021 ◽  
pp. 1-37
Author(s):  
Zhengwu Zhang ◽  
Xiao Wang ◽  
Linglong Kong ◽  
Hongtu Zhu
Keyword(s):  
Quantile Function ◽  
High Dimensional

scholarly journals Probabilistic Prediction of Separation Buffer to Compensate for the Closing Effect on Final Approach

Aerospace ◽  
2021 ◽  
Vol 8 (2) ◽  
pp. 29
Author(s):  
Stanley Förster ◽  
Michael Schultz ◽  
Hartmut Fricke
Keyword(s):  
Quantile Regression ◽  
Prediction Interval ◽  
Quantile Function ◽  
Air Traffic ◽  
Point Estimate ◽  
Probabilistic Prediction ◽  
Traffic System ◽  
Final Approach ◽  
Model Training ◽  
Prediction Approach

The air traffic is mainly divided into en-route flight segments, arrival and departure segments inside the terminal maneuvering area, and ground operations at the airport. To support utilizing available capacity more efficiently, in our contribution we focus on the prediction of arrival procedures, in particular, the time-to-fly from the turn onto the final approach course to the threshold. The predictions are then used to determine advice for the controller regarding time-to-lose or time-to-gain for optimizing the separation within a sequence of aircraft. Most prediction methods developed so far provide only a point estimate for the time-to-fly. Complementary, we see the need to further account for the uncertain nature of aircraft movement based on a probabilistic prediction approach. This becomes very important in cases where the air traffic system is operated at its limits to prevent safety-critical incidents, e.g., separation infringements due to very tight separation. Our approach is based on the Quantile Regression Forest technique that can provide a measure of uncertainty of the prediction not only in form of a prediction interval but also by generating a probability distribution over the dependent variable. While the data preparation, model training, and tuning steps are identical to classic Random Forest methods, in the prediction phase, Quantile Regression Forests provide a quantile function to express the uncertainty of the prediction. After developing the model, we further investigate the interpretation of the results and provide a way for deriving advice to the controller from it. With this contribution, there is now a tool available that allows a more sophisticated prediction of time-to-fly, depending on the specific needs of the use case and which helps to separate arriving aircraft more efficiently.

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