Kernel Density Estimation Model Research Articles

An extended Weight Kernel Density Estimation model forecasts COVID-19 onset risk and identifies spatiotemporal variations of lockdown effects in China

It is important to forecast the risk of COVID-19 symptom onset and thereby evaluate how effectively the city lockdown measure could reduce this risk. This study is a first comprehensive, high-resolution investigation of spatiotemporal heterogeneities on the effect of the Wuhan lockdown on the risk of COVID-19 symptom onset in 347 Chinese cities. An extended Weight Kernel Density Estimation model was developed to predict the COVID-19 onset risk under two scenarios (i.e., with and without the Wuhan lockdown). The Wuhan lockdown, compared with the scenario without lockdown implementation, in general, delayed the arrival of the COVID-19 onset risk peak for 1–2 days and lowered risk peak values among all cities. The decrease of the onset risk attributed to the lockdown was more than 8% in over 40% of Chinese cities, and up to 21.3% in some cities. Lockdown was the most effective in areas with medium risk before lockdown.

Gaussian Mixture Model for the Estimation of Multiyear Solar Irradiance Probability Density

The increasing popularity of photovoltaic resources and the connection of solar farms in larger sizes to power distribution networks make it imperative for network designers to assess the variability of available solar resources at a given location. This is normally achieved by attempting to obtain an accurate estimation of the probability density function (pdf) of solar irradiance at the given site. The parametric beta distribution has long been a popular choice in such studies because of its ease of use. However, pdf estimation using parametric functions can lead to inaccurate models and suboptimal decisions being made about the suitability of potential farm site. In this article, a more robust estimation of solar irradiance pdf than that given by the popular beta distribution is obtained by using a Gaussian mixture model (GMM). Using multiyear solar data, the GMM estimate is also compared with a widely used nonparametric kernel density estimation model that employs a common rule-of-thumb bandwidth selection method. Assessments are carried out using a goodness-of-fit test, three error measures, and the coefficient of determination index. Results demonstrate the improved accuracy and robustness of the GMM, which consistently achieves better performance metrics compared with the kernel density estimation (KDE) model and the beta distribution.

A study of species distribution prediction based on kernel density estimation

The occurrence of Vespa mandarine in the State of Washington is terrible news for the local Western bees, as Vespa mandarine is a very effective predictor. The Washington State government is taking the Vespa mandarine invasion seriously and hopes that people will report it when pests are found. This article processes the sighting reports provided, establishes a model, predicts the potential distribution of coriander, and can effectively provide the possibility of a new report being positive so as to quickly determine the most likely positive report and help the government allocate resources rationally. First, a species distribution prediction model based on kernel density estimation (KDE) was established. We took the Gaussian function as the kernel function, performed KDE on the given data, and controlled the search radius of the kernel function to be 30km from the center of the nest to obtain a probability density heat map reflecting the possibility of coriander spreading to a certain area, which shows that the scope of the spread and the possibility of each location are predictable. It is also essential to consider the circumstances under which the hives are cleared. Therefore, when a hive is removed, we will update the KDE model. If the distance is less than 30km, the point closest to the coordinates of the cleared hive will be deleted.

Mapping cultural ecosystem services using social media data: The case of Datça peninsula

Peyzaj planlamada cesitli karar verme olcekleri, somut ve ekonomik katkiya dâhil olmayan ekosistem hizmetlerinin degerinin olculmesini ve gorsellestirilmesini gerektirir. Kulturel peyzajlarin basarili bir sekilde surdurulmesi ve yonetilmesi icin soyut ve kulturel nitelikteki hizmetlerin, bir baska ifadeyle kulturel ekosistem hizmetlerinin mekânsal dagiliminin anlasilmasi gerekmektedir. Kulturel ekosistem hizmetlerinin sosyal medya verileri kullanilarak modellenmesi, mevcut planlama ve politika araclarina entegre edilebilecek bir yaklasim olusturabilir. Datca Yarimadasi’nda yurutulen bu calismada, uygulama programlama arayuzu (API) araciligiyla Flickr sosyal fotograf agindan indirilen cografi etiketli fotograflar kullanilmis ve kulturel ekosistem hizmetleri haritalanmistir. Fiziksel, deneysel, entelektuel ve sanatsal/ilham verici degerler kapsaminda incelenen fotograflarin; %57’si estetik, %20,1’si sanatsal/ilham verici, %15,4’u kulturel miras ve kimlik degeri, %6,9’u rekreasyonel deger ve %0,7’si ruhani ve dini degerleri gostermektedir. Fotograflara ait cografi etiketler, Kernel yogunluk tahmin modeli ile analiz edilmistir. Analiz sonucunda, kulturel miras ve kimlik degerini yansitan fotograflarin Knidos Antik Kenti ve yakin cevresinde; rekreasyonel deger, estetik deger ve sanatsal/ilham verici degerleri yansitan fotograflarin eski Datca’nin bulundugu Datca Yarimadasi yerlesiminde yogunlasma potansiyeline sahip oldugu ayni zamanda bu potansiyelin yarimada boyunca mekânsal varyasyona sahip olabilecegi gorulmektedir. Ruhani ve dini degerlerin yarimadanin merkezinde yalnizca bir noktada yogunlasabilecegi dikkat cekmektedir. Bu calisma, ekosistem hizmetlerinin haritalanmasi ile ilgili calisan arastirmacilara ulasmayi hedeflemekte ve kulturel degerlerin surdurulebilirliginde peyzaj yonetimi kapsaminda referans olusturabilecek bir yontem akisi sunmaktadir.

Supervised kernel density estimation K-means

K-means is a well-known unsupervised-learning algorithm. It assigns data points to k clusters, the centers of which are termed centroids.However, these centroids have a structure usually represented by a list of quantized vectors, so that kernel density estimation models can better represent complex data distributions. This paper proposes a k-means-based supervised-learning clustering method termed supervised kernel-density-estimation k-means. The proposed approach uses kernel density estimation for class examples inside each cluster to obtain a better representation of the data distribution. The algorithm constructs an initial model using supervised k-means with an equal seed distribution among the classes so that a balance between majority and minority classes is achieved. We also incorporate incremental semi-supervised learning into the proposed method. Experiments were conducted using publicly available benchmark datasets. The results demonstrated that, compared with state-of-the-art supervised methods, the proposed algorithm, which can also perform incremental semi-supervised learning, achieved highly satisfactory performance.

Dezert-Smarandache Theory-Based Fusion for Human Activity Recognition in Body Sensor Networks

Multisensor fusion strategies have been widely applied in human activity recognition (HAR) in body sensor networks (BSNs). However, the sensory data collected by BSNs systems are often uncertain or even incomplete. Thus, designing a robust and intelligent sensor fusion strategy is necessary for high-quality activity recognition. In this article, Dezert–Smarandache theory (DSmT) is used to develop a novel sensor fusion strategy for HAR in BSNs, which can effectively improve the accuracy of recognition. Specifically, in the training stage, the kernel density estimation (KDE)-based models are first built and then precisely selected for each specific activity according to the proposed discriminative functions. After that, a structure of basic belief assignment (BBA) can be constructed, using the relationship between the test data of unknown class and the selected KDE models of all considered types of activities. In order to deal with the conflict between the obtained BBAs, proportional conflict redistribution-6 (PCR6) is applied to fuse the acquired BBAs. Moreover, the missing data of the involved sensors are addressed as ignorance in the framework of the DSmT without manual interpolation or intervention. Experimental studies on two real-world activity recognition datasets (The OPPORTUNITY dataset; Daily and Sports Activity Dataset (DSAD)) are conducted, and the results shows the superiority of our proposed method over some state-of-the-art approaches proposed in the literature.

Efficient Anomaly Detection in a Laser-Surface Heat-Treatment Process via Laser-Spot Tracking

This article proposes a novel algorithm to detect anomalies during a laser-surface heat-treatment process recorded using a high-speed thermal camera. Our approach detects anomalies by tracking the movement of the laser spot along the surface of a production artifact. No previous knowledge of the anomalies is assumed. The model attempts to learn the behavior of a normal process so that anomalous video frames can be detected when the test data differ significantly from the learned model. The model is trained using real process data provided by a company operating in the automotive sector. First, laser-spot movements are obtained by computing a sequence of their positions. Second, the expected movement of the laser spot is accurately determined from the nonanomalous data by using a model based on training multiple kernel density estimation models. Finally, an anomaly score is introduced to classify a workpiece as normal or anomalous using the trained model. Furthermore, our methodology is computationally efficient when compared to other techniques. Additionally, our objective is to perform in-process classification, that is, to perform the classification within a short period after the laser-surface heat-treatment process ends.

The benefits evaluation of abdominal deep inspiration breath hold based on knowledge-based radiotherapy treatment planning for left-sided breast cancer.

PurposeTo study the impact of abdominal deep inspiration breath hold (DIBH) technique on knowledge‐based radiotherapy treatment planning for left‐sided breast cancer to guide the application of DIBH technology.Materials and methodsTwo kernel density estimation (KDE) models were developed based on 40 left‐sided breast cancer patients with two CT acquisitions of free breathing (FB‐CT) and DIBH (DIBH‐CT). Each KDE model was used to predict dose volume histograms (DVHs) based on DIBH‐CT and FB‐CT for another 10 new patients similar to our training datasets. The predicted DVHs were taken as a substitute for dose constraints and objective functions in the Eclipse treatment planning system, with the same requirements for the planning target volume (PTV). The mean doses to the heart, the left anterior descending coronary artery (LADCA) and the ipsilateral lung were evaluated and compared using the T‐test among clinical plans, KDE predictions, and KDE plans.ResultsOur study demonstrated that the KDE model can generate deliverable simulations equivalent to clinically applicable plans. The T‐test was applied to test the consistency hypothesis on another ten left‐sided breast cancer patients. In cases of the same breathing status, there was no statistically significant difference between the predicted and the clinical plans for all clinically relevant DVH indices (P > 0.05), and all predicted DVHs can be transferred into deliverable plans. For DIBH‐CT images, significant differences were observed between FB model predictions and clinical plans (P < 0.05). DIBH model prediction cannot be optimized to a deliverable plan based on FB‐CT, with a counsel of perfection.ConclusionKDE models can predict DVHs well for the same breathing conditions but degrade with different breathing conditions. The benefits of DIBH for a given patient can be evaluated with a quick comparison of prediction results of the two models before treatment planning.

A novel probabilistic short-term wind energy forecasting model based on an improved kernel density estimation

The evolution of renewable energy especially wind energy over the past decade has surpassed all expectations. Short-term probabilistic wind power forecasting is a good option to increase the reliability of power system. But short-term forecasting of power generated by wind turbine has high error due to uncertainty parameter such as wind speed so, it is very important to find a way to increase the accuracy of forecasting. Therefore, in this paper, a novel forecasting method that has high reliability compared to other methods is presented. In this paper, in order to benefit the superiority of various prediction models, a new Improved Kernel Density Estimation (IKDE) method is exploited to estimate the wind energy possibility. The combination of various prediction models and the suggested method might develop the function of probabilistic prediction by supplying divergent types of compactness performance. KDE method is a powerful method to analyze background and foreground characteristic. In order to increase the efficiency of KDE method some of predicting model are combined and a detection algorithm based on an Improved Kernel Density Estimation (IKDE) model is defined. The appropriate bandwidths, comparative threshold, comparative background sample learning array, and an enhanced sample updating model for sample learning array are proposed as the basics of the IKDE model. Two levels of optimization are used to simplify the IKDE model parameters. Finally, in order to prove the superiority of the proposed method over other methods, this method and 4 other methods have been implemented on 10 wind farms. The simulation results show that the prediction accuracy of the proposed method is about 3.8% higher than other methods due to the improved structure.

Likelihood of elephant death risk applying kernel density estimation model along the railway track within biodiversity hotspot of Bhutan–Bengal Himalayan Foothill

The seasonal and occasional movement of wild animals including elephants from one terrestrial habitat to another habitat are very common natural as well as biological habits for the survival of their lives. Around 163 km railway track runs from Siliguri Junction (SGUJ) to Alipurduar Junction (APDJ) within biodiversity hotspot region. According to the report of Forest Department, around 14 prominent and 59 minor elephant corridors have been crisscrossed over the railway track and in between the years 1974 and 2019, nearly 71 elephants are brutally killed due to collision with running trains. The kernel density estimation model is applied to evaluate the spatio-temporal death risk of elephants. To predict the spatial vulnerability or risk of accidental death of elephants, Kernel density estimation analytical algorithms like Bandwidth selection, Intensity, Grid Resolution, Kernel function have been considered. This model considers past accidental deaths data along with secondary data like train speed, fragmentation of elephant habitats, distance of croplands from railway track, human encroachment with electric fencing etc. The anthropogenic activities as well as land use and land cover change have been analysed using Landsat 8 Operational Land Imager—OLI (2019) satellite images and digitally processed by EDRAS IMAGINE 16.5(v16.5.0.852) software. Similarly digital thematic maps have also been prepared on ArcGIS 10.3 platform. Kernel Density Estimation (KDE) intensity (risk) is computed considering the Elephant Death Risk Score (EDRS) as it takes into account of the first and second order properties. Fixed bandwidth is selected for the whole distribution and it is computed by the nearest neighbour distance mean method. On the basis of calculated $$\tau$$ value, (the mean distance between centroids and nearest neighbour index) Kernel Density map is prepared to show the elephant death risk in term of first order properties and second order properties. The result shows very high and high KD (risk) values (0.9799–10.0709) are confined in the eastern and western segments of the SGUJ to APDJ railway line. Therefore, this model helps to take sustainable holistic environmental management of wild animals as well as wild natural habitats in different corners of the globe.

Analyzing traffic violation behavior at urban intersections: A spatio-temporal kernel density estimation approach using automated enforcement system data

The Automated Enforcement System (AES) has become the most important traffic enforcement system in China. In this study, a spatio-temporal kernel density estimation (STKDE) model, integrating spatio-temporal statistics and three-dimensional visualization techniques, was applied to reveal the spatial and temporal patterns of traffic violation behavior at urban intersections. The multivariate Gaussian kernel function was selected for space and time density estimation, as it has been shown to be a good arbitrary probability density function for continuous multivariate data. Because the STKDE model builds a space-time cube that adopts different colors of voxels to visualize the density of traffic violations, an optimal bandwidth selector that combines unconstrained pilot bandwidth matrices with a data-driven method was selected for achieving the best visualization result. The raw AES traffic violation data over 200 weekdays from 69 intersections in the city of Wujiang were empirically analyzed. The results show that the STKDE space-time cube made it easier to detect the spatio-temporal patterns of traffic violations than did the traditional hotspots map. An interesting finding was that traffic sign violations and traffic marking violations were primarily concentrated not in regular peak hours, but during the time period of 14:00-16:00, which indicates that these intersections were the most congested during this period. Primarily, the STKDE model identified seven patterns of spatio-temporal traffic violation hotspots and coldspots. These results are important because their prediction of temporal trends of traffic violations may help contribute toward the understanding and improvement of intersection safety problems.

Modeling the Charging Behaviors for Electric Vehicles Based on Ternary Symmetric Kernel Density Estimation

The accurate modeling of the charging behaviors for electric vehicles (EVs) is the basis for the charging load modeling, the charging impact on the power grid, orderly charging strategy, and planning of charging facilities. Therefore, an accurate joint modeling approach of the arrival time, the staying time, and the charging capacity for the EVs charging behaviors in the work area based on ternary symmetric kernel density estimation (KDE) is proposed in accordance with the actual data. First and foremost, a data transformation model is established by considering the boundary bias of the symmetric KDE in order to carry out normal transformation on distribution to be estimated from all kinds of dimensions to the utmost extent. Then, a ternary symmetric KDE model and an optimum bandwidth model are established to estimate the transformed data. Moreover, an estimation evaluation model is also built to transform simulated data that are generated on a certain scale with the Monte Carlo method by means of inverse transformation, so that the fitting level of the ternary symmetric KDE model can be estimated. According to simulation results, a higher fitting level can be achieved by the ternary symmetric KDE method proposed in this paper, in comparison to the joint estimation method based on the edge KDE and the ternary t-Copula function. Moreover, data transformation can effectively eliminate the boundary effect of symmetric KDE.

A novel method based on lower–upper bound approximation to predict the wind energy

Recently, the prediction of wind power generation has served as a prerequisite problem for determining the objective of the reliability and low–cost power system performance. The difference between conventional deterministic prediction and probabilistic prediction is that the first types ignore the uncertainty of the wind speeds. In this paper, a novel probabilistic prediction method as improved lower–upper bound approximation is applied for building the reliable prediction intervals, which is based on the system that uses the mathematical models of the environment to prognosticate the weather based on existing meteorology (Numeral Weather Prediction System). To verify the worth of the proposed method, forecasting modes in this study are divided as hourly and daily predictions, which are applied to seven wind farms of Taiwan. In addition, adapting parameters in improved lower–upper bound approximation method is performed by resorting to the charged search system algorithm. Also, to increase the prediction speed, the probability density function of wind speed is used, and to decrease the estimation model volume, the kernel density estimation model is applied into the proposed method. The simulation results in comparison with other methods indicate that the prediction intervals produced by the proposed method outperformed and its indices are better. The average error between prediction and real data in the proposed method obtained as about 11%, while other methods error is more than 15%. In addition, three prediction interval indices are used in order to evaluate the different studied manners as: prediction interval overlay probability, normalized average of prediction interval length, and overlay width scale. As the results shown, the best performance is related to the proposed method.

Spatial crime distribution and prediction for sporting events using social media

ABSTRACT Sporting events attract high volumes of people, which in turn leads to increased use of social media. In addition, research shows that sporting events may trigger violent behavior that can lead to crime. This study analyses the spatial relationships between crime occurrences, demographic, socio-economic and environmental variables, together with geo-located Twitter messages and their ‘violent’ subsets. The analysis compares basketball and hockey game days and non-game days. Moreover, this research aims to analyze crime prediction models using historical crime data as a basis and then introducing tweets and additional variables in their role as covariates of crime. First, this study investigates the spatial distribution of and correlation between crime and tweets during the same temporal periods. Feature selection models are applied in order to identify the best explanatory variables. Then, we apply localized kernel density estimation model for crime prediction during basketball and hockey games, and on non-game days. Findings from this study show that Twitter data, and a subset of violent tweets, are useful in building prediction models for the seven investigated crime types for home and away sporting events, and non-game days, with different levels of improvement.

Provincial cultivated land use efficiency in China: Empirical analysis based on the SBM-DEA model with carbon emissions considered

Rapid urbanization and industrialization has worsened the situation of the scarce cultivated land resources of China. It's therefore of great importance for sustainable development based on the systematic evaluation on cultivated land use efficiency (CLUE). This study took carbon emissions resulting from cultivated land use into the measurement framework of CLUE, and a slack-based measure (SBM) model with undesirable outputs, boxplot, kernel density estimation and Tobit regression model are adopted for the analysis of 31 provinces in China from 2000 to 2017. The results showed that there was an increasing trend in CLUE in China from 0.5236 in 2000 to 0.8501 in 2017, with the growth rate of 38.40%. Most of provinces in China have much lower levels of CLUE with significantly spatial disparities. In particular, Hainan, Chongqing, Sichuan and Guizhou are always most efficient with the highest value of 1. At the regional level, the average value of CLUE in the northeastern region is the highest, followed by the western, eastern and central regions, and the CLUE in the eastern region is more unstable than the other three regions. The results of Tobit regression show that natural conditions, cultivated land resource endowments, agricultural production conditions, regional economic development and regional science and technology development are important factors resulting in the disparity of China's CLUE.

Scalable high-resolution forecasting of sparse spatiotemporal events with kernel methods: A winning solution to the NIJ “Real-Time Crime Forecasting Challenge”

We propose a generic spatiotemporal event forecasting method which we developed for the National Institute of Justice’s (NIJ) Real-Time Crime Forecasting Challenge (National Institute of Justice (2017)). Our method is a spatiotemporal forecasting model combining scalable randomized Reproducing Kernel Hilbert Space (RKHS) methods for approximating Gaussian processes with autoregressive smoothing kernels in a regularized supervised learning framework. While the smoothing kernels capture the two main approaches in current use in the field of crime forecasting, kernel density estimation (KDE) and self-exciting point process (SEPP) models, the RKHS component of the model can be understood as an approximation to the popular log-Gaussian Cox Process model. For inference, we discretize the spatiotemporal point pattern and learn a log-intensity function using the Poisson likelihood and highly efficient gradient-based optimization methods. Model hyperparameters including quality of RKHS approximation, spatial and temporal kernel lengthscales, number of autoregressive lags and bandwidths for smoothing kernels as well as cell shape, size and rotation, were learned using cross validation. Resulting predictions significantly exceeded baseline KDE estimates and SEPP models for sparse events.

Probabilistic Optimal Power Flow Calculation Method Based on Adaptive Diffusion Kernel Density Estimation

In order to accurately evaluate the influence of the uncertainty and correlation of photovoltaic (PV) output and load on the running state of power system, a probabilistic optimal power flow calculation method based on adaptive diffusion kernel density estimation is proposed in paper. Firstly, based on the distribution characteristics of PV output, the adaptive diffusion kernel density estimation model of PV output is constructed, which can fit the distribution of arbitrary distribution of PV power. This model can improve the local adaptability of PV output model and reflect the uncertainty and volatility of PV output more accurately. Secondly, The Kendall rank correlation coefficient and the least Euclidean distance are used as correlation measure and index of fitting to select the optimal Copula function, and the joint probability distribution model of PV output and load is constructed. After extracting the correlated PV output and load samples, a probabilistic optimal power flow calculation method considering the correlation of PV output and load is proposed. Finally, simulation studies are conducted with the measured data of a PV power plant of China and the IEEE 30-bus power system. The results show that considering the correlation between PV output and load can improve the accuracy of probabilistic optimal power flow calculation and effectively reduce the power generation cost of power system.

Kernel density estimation model for wind speed probability distribution with applicability to wind energy assessment in China

A kernel density estimation (KDE) model for the probability distribution of wind speed (PDWS) is proposed in this paper for application to wind energy assessment (WEA) in China. Four bandwidth selectors, including normal scale (NS), plug in, biased cross-validation, and least-square cross validation, are proposed for the KDE model. Popular parametric distribution models are also introduced for comparisons with the KDE models. Based on five-year day-average wind speed data from 698 nationwide wind stations in China, the performance and robustness of both parametric and KDE models were evaluated comprehensively on the regional scale. Wind power density (WPD) and wind turbine power output (WTPO), which are the priorities in WEA, are subsequently calculated based on the estimated PDWS models. The ranking results of four individual metrics and one comprehensive metric indicate that the four KDE models outperform the parametric models in fitting the PDWS. The KDE-NS model performs the best compared to the other three KDE models. In addition to the KDE models, the generalized gamma and generalized extreme values were considered as better parametric models in fitting the PDWS. KDE models also performed well in WPD estimation, especially the KDE-NS model with a mean absolute percentage error (MAPE) value as low as 2%. Some parametric models, i.e., Johnson SB and Wakeby, which are not outstanding in PDWS fitting, however perform well in WPD estimation, and their MAPE values can be controlled to remain within 3%. This indicates that the result of the PDWS is not completely equivalent to that of WPD estimation. The WPD and WTPO in most of China's interior areas are less than 40W/m2 and 1.2 GWh, respectively. In the eastern coastal areas, middle and eastern Inner Mongolia, and some western provinces, the WPD and WTPO are relatively higher, and can reach or exceed 240W/m2 and 3.5 GWh, respectively.

Wind speed probability density estimation using root-transformed local linear regression

Despite the many attractive features of wind-based renewables, the intermittency of wind generation stands out as a critical challenge. An accurate and reliable nonparametric wind speed probability density model is proposed in this paper based on the application of local linear regression in tandem with a root transformation method, introduced here for the first time. The proposed root-transformed local linear regression approach provides a robust estimate of wind speed distribution and produces more accurate results than kernel density estimation models. The performance of the root-transformed local linear regression estimator is assessed via comparisons with three popular parametric models (Rayleigh, Weibull and Gaussian distributions), two additional parametric models (Birnbaum–Saunders and Nakagami distributions) recently suggested for wind speed probability density estimation, and two nonparametric kernel density estimation models using two standard goodness-of-fit hypothesis tests (Chi-squared and Kolmogorov–Smirnov), coefficient of determination and two error metrics (root mean square error and mean absolute error). Results confirm the accuracy of the proposed root-transformed local linear regression estimator for modelling wind speed probability density, with substantial improvements in all error metrics over parametric and kernel density estimation models.

Root-Transformed Local Linear Regression for Solar Irradiance Probability Density Estimation

Solar energy is one of the most important and widely utilized renewable energy resource. Despite the many attractive features of solar-based renewables, the wide scale integration of solar generation into electric power systems presents significant challenges to network planners and operators, mainly due to the intermittent nature of solar energy. Most published work in this area is, however, focused on short-term forecasting studies used for unit commitment and energy market decisions with very little attention paid to solar irradiance probability density estimation needed for network planning and design studies. In this paper, a reliable nonparametric model of solar irradiance probability density is proposed based on the application of local linear regression in tandem with a root transformation method, introduced here for the first time. The performance of the proposed estimator is assessed via comparisons with the parametric Beta distribution (conventionally employed to model solar irradiance probability density) and two nonparametric kernel density estimation models; using the Kolmogorov–Smirnov (K–S) goodness-of-fit test, coefficient of determination ( $R^2$ ), and a number of error metrics. Results confirm the suitability and accuracy of the proposed method for solar irradiance probability density estimation.