scholarly journals Modeling the Distribution of Precipitation Forecasts from the Canadian Ensemble Prediction System Using Kernel Density Estimation

2008 ◽  
Vol 23 (4) ◽  
pp. 575-595 ◽  
Author(s):  
Syd Peel ◽  
Laurence J. Wilson
Keyword(s):  
Probability Density ◽  
Density Estimation ◽  
Kernel Density Estimation ◽  
Probabilistic Models ◽  
Kernel Density ◽  
Random Variable ◽  
Ensemble Prediction ◽  
Prediction System ◽  
Ensemble Prediction System ◽  
Density Estimators

Abstract Kernel density estimation is employed to fit smooth probabilistic models to precipitation forecasts of the Canadian ensemble prediction system. An intuitive nonparametric technique, kernel density estimation has become a powerful tool widely used in the approximation of probability density functions. The density estimators were constructed using the gamma kernels prescribed by S.-X. Chen, confined as they are to the nonnegative real axis, which constitutes the support of the random variable representing precipitation accumulation. Performance of kernel density estimators for several different smoothing bandwidths is compared with the discrete probabilistic model obtained as the fraction of member forecasts predicting the events, which for this study consisted of threshold exceedances. A propitious choice of the smoothing bandwidth yields smooth forecasts comparable, or sometimes superior, to the discrete probabilistic forecast, depending on the character of the raw ensemble forecasts. At the same time more realistic models of the probability density are achieved, particularly in the tail of the distribution, yielding forecasts that can be optimally calibrated for extreme events.

scholarly journals Benchmarking the reliability of medium-voltage lines

2017 ◽  
Vol 68 (3) ◽  
pp. 212-215 ◽  
Author(s):  
Michal Kolcun ◽  
Mirosław Kornatka ◽  
Anna Gawlak ◽  
Zsolt Čonka
Keyword(s):  
Density Distribution ◽  
Probability Density ◽  
Density Estimation ◽  
Kernel Density Estimation ◽  
Kernel Density ◽  
Power Lines ◽  
Probability Density Distribution ◽  
Nonparametric Method ◽  
Medium Voltage

Abstract This paper discusses the problem of reliability of the Polish medium voltage power lines. It presents the benchmarking of power lines and values of SAIDI. The probability density distribution of the medium voltage lines length as well as selected indicators of the MV power lines reliability, being operated by the distribution companies under test, are also introduced. The analysis is based on the actual MV lines and uses the nonparametric method of kernel density estimation.

scholarly journals Forecasting Hourly Power Load Considering Time Division: A Hybrid Model Based on K-means Clustering and Probability Density Forecasting Techniques

2019 ◽  
Vol 11 (24) ◽  
pp. 6954
Author(s):  
Fuqiang Li ◽  
Shiying Zhang ◽  
Wenxuan Li ◽  
Wei Zhao ◽  
Bingkang Li ◽  
...  
Keyword(s):  
Probability Density ◽  
Density Estimation ◽  
Kernel Density Estimation ◽  
Clustering Algorithm ◽  
Estimation Method ◽  
Kernel Density ◽  
Support Vector ◽  
Average Width ◽  
Power Load ◽  
Density Forecasting

In comparison with traditional point forecasting method, probability density forecasting can reflect the load fluctuation more effectively and provides more information. This paper proposes a hybrid hourly power load forecasting model, which integrates K-means clustering algorithm, Salp Swarm Algorithm (SSA), Least Square Support Vector Machine (LSSVM), and kernel density estimation (KDE) method. Firstly, the loads at 24 times a day are grouped into three categories according to the K-means clustering algorithm, which correspond to the valley period, flat period, and peak period of the load, respectively. Secondly, the load point forecasting value is obtained by LSSVM method optimized by SSA algorithm. Furthermore, the kernel density estimation method is employed to fit the forecasting error of SSA-LSSVM in different time periods, and the probability density function of the error distribution is obtained. The final load probability density forecasting result is obtained by combining the point forecasting value and the error fitting result, and then the upper and lower limits of the confidence interval under the given confidence level are solved. In this paper, the performance of the model is evaluated by two indicators named interval coverage and interval average width. Meanwhile, in comparison with several other models, it can be concluded that the proposed model can effectively improve the forecasting effect.

A Statistical Model for Wind Power Forecast Error Based on Kernel Density Estimation

2014 ◽  
Vol 8 (1) ◽  
pp. 501-507
Author(s):  
Liyang Liu ◽  
Junji Wu ◽  
Shaoliang Meng
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Wind Power ◽  
Density Estimation ◽  
Kernel Density Estimation ◽  
Forecast Error ◽  
Kernel Density ◽  
Wind Power Forecast ◽  
Proposed Model ◽  
Chi Squared

Wind power has been developed rapidly as a clean energy in recent years. The forecast error of wind power, however, makes it difficult to use wind power effectively. In some former statistical models, the forecast error was usually assumed to be a Gaussian distribution, which had proven to be unreliable after a statistical analysis. In this paper, a more suitable probability density function for wind power forecast error based on kernel density estimation was proposed. The proposed model is a non-parametric statistical algorithm and can directly obtain the probability density function from the error data, which do not need to make any assumptions. This paper also presented an optimal bandwidth algorithm for kernel density estimation by using particle swarm optimization, and employed a Chi-squared test to validate the model. Compared with Gaussian distribution and Beta distribution, the mean squared error and Chi-squared test show that the proposed model is more effective and reliable.

Nonparametric frequency polygon estimation for modeling input data

2019 ◽  
Author(s):  
Stephen Hague ◽  
Simaan AbouRizk
Keyword(s):  
Density Estimation ◽  
Kernel Density Estimation ◽  
Posterior Distribution ◽  
Input Data ◽  
Probability Distributions ◽  
Kernel Density ◽  
Simulation Environment ◽  
Frequency Polygon ◽  
Density Estimators

To construct valid probability distributions solely from input data, this paper compares three nonparametric density estimators: (1) histograms, (2) Kernel Density Estimation, and (3) Frequency Polygon Estimation. A pseudocode is implemented, a practical example is illustrated, and the Simphony.NET simulation environment is used to fit the nonparametric frequency polygon to a set of data to recreate it as a posterior distribution via the Metropolis-Hastings algorithm.

scholarly journals Verification of an Ensemble Prediction System against Observations

2007 ◽  
Vol 135 (7) ◽  
pp. 2688-2699 ◽  
Author(s):  
G. Candille ◽  
C. Côté ◽  
P. L. Houtekamer ◽  
G. Pellerin
Keyword(s):  
Confidence Intervals ◽  
Forecast Error ◽  
Random Variable ◽  
Ensemble Prediction ◽  
Systematic Bias ◽  
Prediction System ◽  
Ensemble Prediction System ◽  
Continuous Ranked Probability Score ◽  
Verification System ◽  
Verification Methodology

Abstract A verification system has been developed for the ensemble prediction system (EPS) at the Canadian Meteorological Centre (CMC). This provides objective criteria for comparing two EPSs, necessary when deciding whether or not to implement a new or revised EPS. The proposed verification methodology is based on the continuous ranked probability score (CRPS), which provides an evaluation of the global skill of an EPS. Its reliability/resolution partition, proposed by Hersbach, is used to measure the two main attributes of a probabilistic system. Also, the characteristics of the reliability are obtained from the two first moments of the reduced centered random variable (RCRV), which define the bias and the dispersion of an EPS. Resampling bootstrap techniques have been applied to these scores. Confidence intervals are thus defined, expressing the uncertainty due to the finiteness of the number of realizations used to compute the scores. All verifications are performed against observations to provide more independent validations and to avoid any local systematic bias of an analysis. A revised EPS, which has been tested at the CMC in a parallel run during the autumn of 2005, is described in this paper. This EPS has been compared with the previously operational one with the verification system presented above. To illustrate the verification methodology, results are shown for the temperature at 850 hPa. The confidence intervals are computed by taking into account the spatial correlation of the data and the temporal autocorrelation of the forecast error. The revised EPS performs significantly better for all the forecast ranges, except for the resolution component of the CRPS where the improvement is no longer significant from day 7. The significant improvement of the reliability is mainly due to a better dispersion of the ensemble. Finally, the verification system correctly indicates that variations are not significant when two theoretically similar EPSs are compared.

scholarly journals Probability Density Forecasting of Wind Speed Based on Quantile Regression and Kernel Density Estimation

Energies ◽  
2020 ◽  
Vol 13 (22) ◽  
pp. 6125
Author(s):  
Lei Zhang ◽  
Lun Xie ◽  
Qinkai Han ◽  
Zhiliang Wang ◽  
Chen Huang
Keyword(s):  
Wind Speed ◽  
Quantile Regression ◽  
Probability Density ◽  
Density Estimation ◽  
Kernel Density Estimation ◽  
Confidence Level ◽  
Kernel Density ◽  
Conditional Quantiles ◽  
Wind Speeds ◽  
Density Forecasting

Based on quantile regression (QR) and kernel density estimation (KDE), a framework for probability density forecasting of short-term wind speed is proposed in this study. The empirical mode decomposition (EMD) technique is implemented to reduce the noise of raw wind speed series. Both linear QR (LQR) and nonlinear QR (NQR, including quantile regression neural network (QRNN), quantile regression random forest (QRRF), and quantile regression support vector machine (QRSVM)) models are, respectively, utilized to study the de-noised wind speed series. An ensemble of conditional quantiles is obtained and then used for point and interval predictions of wind speed accordingly. After various experiments and comparisons on the real wind speed data at four wind observation stations of China, it is found that the EMD-LQR-KDE and EMD-QRNN-KDE generally have the best performance and robustness in both point and interval predictions. By taking conditional quantiles obtained by the EMD-QRNN-KDE model as the input, probability density functions (PDFs) of wind speed at different times are obtained by the KDE method, whose bandwidth is optimally determined according to the normal reference criterion. It is found that most actual wind speeds lie near the peak of predicted PDF curves, indicating that the probabilistic density prediction by EMD-QRNN-KDE is believable. Compared with the PDF curves of the 90% confidence level, the PDF curves of the 80% confidence level usually have narrower wind speed ranges and higher peak values. The PDF curves also vary with time. At some times, they might be biased, bimodal, or even multi-modal distributions. Based on the EMD-QRNN-KDE model, one can not only obtain the specific PDF curves of future wind speeds, but also understand the dynamic variation of density distributions with time. Compared with the traditional point and interval prediction models, the proposed QR-KDE models could acquire more information about the randomness and uncertainty of the actual wind speed, and thus provide more powerful support for the decision-making work.

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