scholarly journals Data bank: nine numerical methods for determining the parameters of weibull for wind energy generation tested by five statistical tools

2021 ◽  
Vol 12 (2) ◽  
pp. 1114
Author(s):  
Ahmed Samir Badawi ◽  
Siti Hajar Yusoff ◽  
Alhareth Mohammed Zyoud ◽  
Sheroz Khan ◽  
Aisha Hashim ◽  
...  
Keyword(s):  
Maximum Likelihood ◽  
Numerical Methods ◽  
Root Mean Square Error ◽  
Mean Square Error ◽  
Root Mean Square ◽  
Prediction Accuracy ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Mean Square ◽  
Modified Maximum Likelihood

This study aims to determine the potential of wind energy in the mediterranean coastal plain of Palestine. The parameters of the Weibull distribution were calculated on basis of wind speed data. Accordingly, two approaches were employed: analysis of a set of actual time series data and theoretical Weibull probability function. In this analysis, the parameters Weibull shape factor ‘<em>k</em>’ and the Weibull scale factor ‘<em>c</em>’ were adopted. These suitability values were calculated using the following popular methods: method of moments (MM), standard deviation method (STDM), empirical method (EM), maximum likelihood method (MLM), modified maximum likelihood method (MMLM), second modified maximum likelihood method (SMMLM), graphical method (GM), least mean square method (LSM) and energy pattern factor method (EPF). The performance of these numerical methods was tested by root mean square error (RMSE), index of agreement (IA), Chi-square test (X<sup>2</sup>), mean absolute percentage error (MAPE) and relative root mean square error (RRMSE) to estimate the percentage of error. Among the prediction techniques. The EPF exhibited the greatest accuracy performance followed by MM and MLM, whereas the SMMLM exhibited the worst performance. The RMSE achieved the best prediction accuracy, whereas the RRMSE attained the worst prediction accuracy.

scholarly journals اقتراح استعمال مبدأ اعظم دالة انتروبي POME على توزيع كاما العام في تقدير احتمالات البقاء للسكان في العراق

2016 ◽  
Vol 22 (93) ◽  
pp. 454
Author(s):  
عمر عبد المحسن علي ◽  
رغدة زياد طارق
Keyword(s):  
Maximum Likelihood ◽  
Root Mean Square Error ◽  
Mean Square Error ◽  
Root Mean Square ◽  
Mean Square ◽  
Percent Error ◽  
Mean Absolute Percent Error ◽  
Generalized Gamma ◽  
Economic Survey ◽  
Absolute Percent Error

المستخلص: تم في هذا البحث تقدير دالة البقاء على قيد الحياة لبيانات تعاني من اضطراب وتشويش للمسح الاجتماعي والاقتصادي للأسرة في العراق 2012 (Iraq Household Socio-Economic Survey: IHSES II 2012) لبيانات فئات خماسية العمر تتبع توزيع كاما العام (Generalized Gamma: GG). واستعملت طريقتين للأغراض التقدير والموائمة fitting وهي طريقة مبدأ اعظم دالة انتروبي Principle of Maximizing Entropy: POME  وطريقة تمهيد لامعلمية بدالة لبّية Kernel ، للتغلب على المشاكل الرياضية التي تعتري التكاملات التي يتضمنها هذا التوزيع بالذات المتمثلة بتكامل دالة كاما الناقص، هذا الى جانب استعمال الطريقة التقليدية وهي الامكان الاعظم Maximum Likelihood: ML حيث تتم المقارنة على اساس اسلوب الجهاز المركزي للإحصاء في احتساب دالة البقاء من خلال برنامج MORTPAK كقيم حقيقية. وبعد ذلك القيام بالمقارنة باستعمال معيار جذر متوسط مربعات الخطأ Root Mean Square Error: RMSE  ، ومعيار متوسط مطلق نسبة الخطأ Mean Absolute Percent Error: MAPE  . وأظهرت النتائج أفضلية طريقة الانتروبي في تقدير دالة البقاء على الطرائق الاخرى.  

scholarly journals Best estimation for the Reliability of 2-parameter Weibull Distribution

2009 ◽  
Vol 6 (4) ◽  
pp. 705-710
Author(s):  
Baghdad Science Journal
Keyword(s):  
Maximum Likelihood ◽  
Weibull Distribution ◽  
Mean Square Error ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Statistical Criterion ◽  
Mean Square ◽  
Simulation Process ◽  
The Mean ◽  
Two Parameter

This Research Tries To Investigate The Problem Of Estimating The Reliability Of Two Parameter Weibull Distribution,By Using Maximum Likelihood Method, And White Method. The Comparison Is done Through Simulation Process Depending On Three Choices Of Models (?=0.8 , ß=0.9) , (?=1.2 , ß=1.5) and (?=2.5 , ß=2). And Sample Size n=10 , 70, 150 We Use the Statistical Criterion Based On the Mean Square Error (MSE) For Comparison Amongst The Methods.

scholarly journals Numerical daemons of hydrological models are summoned by extreme precipitation

2021 ◽  
Vol 25 (10) ◽  
pp. 5425-5446
Author(s):  
Peter T. La Follette ◽  
Adriaan J. Teuling ◽  
Nans Addor ◽  
Martyn Clark ◽  
Koen Jansen ◽  
...  
Keyword(s):  
Numerical Methods ◽  
Root Mean Square Error ◽  
Mean Square Error ◽  
Root Mean Square ◽  
Extreme Precipitation ◽  
Computational Cost ◽  
Numerical Error ◽  
Mean Square ◽  
Hydrological Models ◽  
Numerical Techniques

Abstract. Hydrological models are usually systems of nonlinear differential equations for which no analytical solutions exist and thus rely on numerical solutions. While some studies have investigated the relationship between numerical method choice and model error, the extent to which extreme precipitation such as that observed during hurricanes Harvey and Katrina impacts numerical error of hydrological models is still unknown. This knowledge is relevant in light of climate change, where many regions will likely experience more intense precipitation. In this experiment, a large number of hydrographs are generated with the modular modeling framework FUSE (Framework for Understanding Structural Errors), using eight numerical techniques across a variety of forcing data sets. All constructed models are conceptual and lumped. Multiple model structures, parameter sets, and initial conditions are incorporated for generality. The computational cost and numerical error associated with each hydrograph were recorded. Numerical error is assessed via root mean square error and normalized root mean square error. It was found that the root mean square error usually increases with precipitation intensity and decreases with event duration. Some numerical methods constrain errors much more effectively than others, sometimes by many orders of magnitude. Of the tested numerical methods, a second-order adaptive explicit method is found to be the most efficient because it has both a small numerical error and a low computational cost. A small literature review indicates that many popular modeling codes use numerical techniques that were suggested by this experiment to be suboptimal. We conclude that relatively large numerical errors may be common in current models, highlighting the need for robust numerical techniques, in particular in the face of increasing precipitation extremes.

scholarly journals Comparing Parameter Estimation of Random Coefficient Autoregressive Model by Frequentist Method

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 62 ◽  
Author(s):  
Autcha Araveeporn
Keyword(s):  
Maximum Likelihood ◽  
Least Squares ◽  
Mean Square Error ◽  
Maximum Likelihood Method ◽  
Least Squares Method ◽  
Likelihood Function ◽  
Likelihood Method ◽  
Mean Square ◽  
Average Mean Square Error ◽  
Frequentist Method

This paper compares the frequentist method that consisted of the least-squares method and the maximum likelihood method for estimating an unknown parameter on the Random Coefficient Autoregressive (RCA) model. The frequentist methods depend on the likelihood function that draws a conclusion from observed data by emphasizing the frequency or proportion of the data namely least squares and maximum likelihood methods. The method of least squares is often used to estimate the parameter of the frequentist method. The minimum of the sum of squared residuals is found by setting the gradient to zero. The maximum likelihood method carries out the observed data to estimate the parameter of a probability distribution by maximizing a likelihood function under the statistical model, while this estimator is obtained by a differential parameter of the likelihood function. The efficiency of two methods is considered by average mean square error for simulation data, and mean square error for actual data. For simulation data, the data are generated at only the first-order models of the RCA model. The results have shown that the least-squares method performs better than the maximum likelihood. The average mean square error of the least-squares method shows the minimum values in all cases that indicated their performance. Finally, these methods are applied to the actual data. The series of monthly averages of the Stock Exchange of Thailand (SET) index and daily volume of the exchange rate of Baht/Dollar are considered to estimate and forecast based on the RCA model. The result shows that the least-squares method outperforms the maximum likelihood method.

scholarly journals On the Estimation of Parameter of Weighted Sums of Exponential Distribution

2014 ◽  
Vol 2014 ◽  
pp. 1-3
Author(s):  
N. Abbasi ◽  
A. Namju ◽  
N. Safari
Keyword(s):  
Maximum Likelihood ◽  
Exponential Distribution ◽  
Mean Square Error ◽  
Moment Method ◽  
Maximum Likelihood Method ◽  
Random Variable ◽  
Likelihood Method ◽  
Weighted Sums ◽  
Mean Square ◽  
The Mean

The random variable Zn,α=Y1+2αY2+⋯+nαYn, with α∈ℝ and Y1,Y2,…  being independent exponentially distributed random variables with mean one, is considered. Van Leeuwaarden and Temme (2011) attempted to determine good approximation of the distribution of Zn,α. The main problem is estimating the parameter α that has the main state in applicable research. In this paper we show that estimating the parameter α by using the relation between α and mode is available. The mean square error values are obtained for estimating α by mode, moment method, and maximum likelihood method.

Metaheuristic data fitting methods to estimate Weibull parameters for wind speed data: a case study of Hasan Polatkan Airport

2021 ◽  
pp. 1-33
Author(s):  
A. Kaba ◽  
A. E. Suzer
Keyword(s):  
Wind Speed ◽  
Numerical Methods ◽  
Root Mean Square Error ◽  
Objective Function ◽  
Mean Square Error ◽  
Root Mean Square ◽  
Statistical Tests ◽  
Mean Square ◽  
Flight Delays

ABSTRACT Flight delays may be decreased in a predictable way if the Weibull wind speed parameters of a runway, which are an important aspect of safety during the take-off and landing phases of aircraft, can be determined. One aim of this work is to determine the wind profile of Hasan Polatkan Airport (HPA) as a case study. Numerical methods for Weibull parameter determination perform better when the average wind speed estimation is the main objective. In this paper, a novel objective function that minimises the root-mean-square error by employing the cumulative distribution function is proposed based on the genetic algorithm and particle swarm optimisation. The results are compared with well-known numerical methods, such as maximum-likelihood estimation, the empirical method, the graphical method and the equivalent energy method, as well as the available objective function. Various statistical tests in the literature are applied, such as R2, Root-Mean-Square Error (RMSE) and $\chi$ 2. In addition, the Mean Absolute Error (MAE) and total elapsed time calculated using the algorithms are compared. According to the results of the statistical tests, the proposed methods outperform others, achieving scores as high as 0.9789 and 0.9996 for the R2 test, as low as 0.0058 and 0.0057 for the RMSE test, 0.0036 and 0.0045 for the MAE test and 3.53 × 10−5 and 3.50 × 10−5 for the $\chi$ 2 test. In addition, the determination of the wind speed characteristics at HPA show that low wind speed characteristics and regimes throughout the year offer safer take-off and landing schedules for target aircraft. The principle aim of this paper is to help establish the correct orientation of new runways at HPA and maximise the capacity of the airport by minimising flight delays, which represent a significant impediment to air traffic flow.

Ill-Condition Controlled Maximum Likelihood Registration for Multiple Sensors

2014 ◽  
Vol 898 ◽  
pp. 797-801 ◽  
Author(s):  
Xu Guang Yang ◽  
Yue Wang ◽  
Xiu Ming Shan
Keyword(s):  
Maximum Likelihood ◽  
Root Mean Square Error ◽  
Mean Square Error ◽  
Root Mean Square ◽  
Sensor Fusion ◽  
Fusion System ◽  
Mean Square ◽  
Multiple Sensors ◽  
Sensor Registration ◽  
Ill Conditioning

Sensor registration plays an important role in multi-sensor fusion system. In practical scenarios, the performance of traditional registration algorithms degrades when the measurements are closely positioned. In this paper, we point out and analyze the ill-conditioning problem of multi-sensor maximum likelihood registration (MLR) algorithm. Then we propose an ill-condition controlled maximum likelihood registration (ICMLR) algorithm, which can solve the ill-conditioning problem by the technique of diagonal loading. Compared with MLR, the proposed algorithm demonstrates the advantages in both bias estimates and target state estimates in terms of the root mean square error (RMSE) criterion.

Discrimination of Gentiana rigescens from Different Origins by Fourier Transform Infrared Spectroscopy Combined with Chemometric Methods

2015 ◽  
Vol 98 (1) ◽  
pp. 22-26 ◽  
Author(s):  
Yanli Zhao ◽  
Ji Zhang ◽  
Hang Jin ◽  
Jinyu Zhang ◽  
Tao Shen ◽  
...  
Keyword(s):  
Root Mean Square Error ◽  
Ftir Spectroscopy ◽  
Mean Square Error ◽  
Root Mean Square ◽  
Principal Components ◽  
Prediction Accuracy ◽  
Mean Square ◽  
Chemometric Methods ◽  
Contribution Rate ◽  
Gentiana Rigescens

Abstract Gentiana rigescens (“DianLongdan” in Chinese) medicinal plant is usually used for its activities of liver protection, cholagogic, anti-inflammatory, anti-fungal, anti-hyperthyroidism, anti-hypertension, hyperglycemia, and relieving spasm and pain. In this study, methods for thediscrimination of different geographical origins of G. rigescens by FTIR spectroscopy in hyphenation with chemometric methods were developed. Different pretreatments including standard normalvariate, multiplicative scatter correction, first orsecond derivative, Savitzky-Golay filter, and Norrisderivative filter were applied on the spectra to optimize the calibrations. According to spectrum SD, spectrum ranges (3559–2709 and 2026–756 cm–1) were selected, and principalcomponent analysis-Mahalanobis distance (PCA-MD) model was built [the cumulative contribution rate of the first 10 principal components, determination coefficient (R2), root-mean-square error of calibration (RMSEC), and root-mean-square error of prediction (RMSEP), and prediction accuracy were 96.4%,98.6%, 0.5031, 0.7758, and 96.23%, respectively]. The spectral regions (3791–3442, 3043–2765, and 2013–646 cm–1) wereselected by using the variable importance in projection, and partial least squares discriminant analysis(PLS-DA) model was built (the cumulative contribution rate of the first 10 principal components, R2, RMSEC, RMSEP, and prediction accuracy were 91.3%, 92.0%, 0.1171, 0.1806, and 100%, respectively). This research showed that FTIR spectroscopy in combination with chemometrics methods (PCA-MD and PLS-DA) was suitable for the discrimination of different geographical origins of G. rigescens. Furthermore, it was found that PLS-DA provided better results than PCA-MD.

scholarly journals Estimation of Apple Flowering Frost Loss for Fruit Yield Based on Gridded Meteorological and Remote Sensing Data in Luochuan, Shaanxi Province, China

2021 ◽  
Vol 13 (9) ◽  
pp. 1630
Author(s):  
Yaohui Zhu ◽  
Guijun Yang ◽  
Hao Yang ◽  
Fa Zhao ◽  
Shaoyu Han ◽  
...  
Keyword(s):  
Remote Sensing ◽  
Root Mean Square Error ◽  
Mean Square Error ◽  
Root Mean Square ◽  
Minimum Temperature ◽  
Price Regulation ◽  
Flowering Period ◽  
Mean Square ◽  
Prevention Measures ◽  
Agricultural Insurance

With the increase in the frequency of extreme weather events in recent years, apple growing areas in the Loess Plateau frequently encounter frost during flowering. Accurately assessing the frost loss in orchards during the flowering period is of great significance for optimizing disaster prevention measures, market apple price regulation, agricultural insurance, and government subsidy programs. The previous research on orchard frost disasters is mainly focused on early risk warning. Therefore, to effectively quantify orchard frost loss, this paper proposes a frost loss assessment model constructed using meteorological and remote sensing information and applies this model to the regional-scale assessment of orchard fruit loss after frost. As an example, this article examines a frost event that occurred during the apple flowering period in Luochuan County, Northwestern China, on 17 April 2020. A multivariable linear regression (MLR) model was constructed based on the orchard planting years, the number of flowering days, and the chill accumulation before frost, as well as the minimum temperature and daily temperature difference on the day of frost. Then, the model simulation accuracy was verified using the leave-one-out cross-validation (LOOCV) method, and the coefficient of determination (R2), the root mean square error (RMSE), and the normalized root mean square error (NRMSE) were 0.69, 18.76%, and 18.76%, respectively. Additionally, the extended Fourier amplitude sensitivity test (EFAST) method was used for the sensitivity analysis of the model parameters. The results show that the simulated apple orchard fruit number reduction ratio is highly sensitive to the minimum temperature on the day of frost, and the chill accumulation and planting years before the frost, with sensitivity values of ≥0.74, ≥0.25, and ≥0.15, respectively. This research can not only assist governments in optimizing traditional orchard frost prevention measures and market price regulation but can also provide a reference for agricultural insurance companies to formulate plans for compensation after frost.

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