scholarly journals Development of Hartigan’s Dip Statistic with Bimodality Coefficient to Assess Multimodality of Distributions

2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Young-Jin Kang ◽  
Yoojeong Noh
Keyword(s):  
Wind Speed ◽  
Random Variables ◽  
Statistical Simulation ◽  
Link Function ◽  
Multimodal Distribution ◽  
Significance Level ◽  
Engineering Data ◽  
Multimodal Distributions ◽  
Estimation Of Distributions ◽  
Skewness And Kurtosis

In general, although some random variables such as wind speed, temperature, and load are known to have multimodal distributions, input or output random variables are considered to follow unimodal distributions without assessing the unimodality or multimodality of distributions from samples. In uncertainty analysis, estimating unimodal distribution as multimodal distribution or vice versa can lead to erroneous analysis results. Thus, whether a distribution is unimodal or multimodal must be assessed before the estimation of distributions. In this paper, the bimodality coefficient (BC) and Hartigan’s dip statistic (HDS), which are representative methods for assessing multimodality, are introduced and compared. Then, a combined HDS with BC method is proposed. The proposed method has the advantages of both BC and HDS by using the skewness and kurtosis of samples as well as the dip statistic through a link function between the BC values in BC and significance level in HDS. To verify the performance of the proposed method, statistical simulation tests were conducted to evaluate the multimodality for various unimodal, bimodal, and trimodal models. The implementation of the proposed method to real engineering data is shown through case studies. The results demonstrate that the proposed method is more accurate, robust, and reliable than the BC and original HDS alone.

scholarly journals Wind speed variability between 10 and 116 m height from the regional reanalysis COSMO-REA6 compared to wind mast measurements over Northern Germany and the Netherlands

2016 ◽  
Vol 13 ◽  
pp. 151-161 ◽  
Author(s):  
Michael Borsche ◽  
Andrea K. Kaiser-Weiss ◽  
Frank Kaspar
Keyword(s):  
Wind Speed ◽  
The Netherlands ◽  
Diurnal Cycle ◽  
Correlation Coefficients ◽  
Wind Fields ◽  
Northern Germany ◽  
Significance Level ◽  
The North ◽  
The Mean ◽  
Regional Reanalysis

Abstract. Hourly and monthly mean wind speed and wind speed variability from the regional reanalysis COSMO-REA6 is analysed in the range of 10 to 116 m height above ground. Comparisons with independent wind mast measurements performed between 2001 and 2010 over Northern Germany over land (Lindenberg), the North Sea (FINO platforms), and The Netherlands (Cabauw) show that the COSMO-REA6 wind fields are realistic and at least as close to the measurements as the global atmospheric reanalyses (ERA20C and ERA-Interim) on the monthly scale. The median wind profiles of the reanalyses were found to be consistent with the observed ones. The mean annual cycles of variability are generally reproduced from 10 up to 116 m in the investigated reanalyses. The mean diurnal cycle is represented qualitatively near the ground by the reanalyses. At 100 m height, there is little diurnal cycle left in the global and regional reanalyses, though a diurnal cycle is still present in the measurements over land. Correlation coefficients between monthly means of the observations and the reanalyses range between 0.92 at 10 m and 0.99 at 116 m, with a slightly higher correlation of the regional reanalyses at Lindenberg at 10 m height which is significant only at a lower than 95 % significance level. Correlations of daily means tend to be higher for the regional reanalysis COSMO-REA6. Increasing temporal resolution further, reduces this advantage of the regional reanalysis. At around 100 m, ERA-Interim yields a higher correlation at Lindenberg and Cabauw, whereas COSMO-REA6 yields a higher correlation at FINO1 and FINO2.

Reliability analysis for a spar-supported floating offshore wind turbine

2017 ◽  
Vol 42 (1) ◽  
pp. 51-65 ◽  
Author(s):  
Abhinav Sultania ◽  
Lance Manuel
Keyword(s):  
Wind Speed ◽  
Wind Turbine ◽  
Reliability Analysis ◽  
Wave Height ◽  
Return Period ◽  
Random Variables ◽  
Environmental Data ◽  
First Order Reliability Method ◽  
First Order ◽  
Reliability Method

The reliability analysis of a spar-supported floating offshore 5-MW wind turbine is the subject of this study. Environmental data from a selected site are employed in the numerical studies. Using time-domain simulations, the dynamic behavior of a coupled platform-turbine system is studied; statistics of tower and rotor loads as well as platform motions are estimated and critical combinations of wind speed and wave height identified. Long-term loads associated with a 50-year return period are estimated using statistical extrapolation based on loads derived from simulations. Inverse reliability procedures that seek appropriate fractile levels for underlying variables consistent with the target load return period are employed; these include use of (1) two-dimensional inverse first-order reliability method where extreme loads, conditional on wind speed and wave height random variables, are selected at median levels and (2) three-dimensional inverse first-order reliability method where variability in the environmental and load random variables is fully represented.

scholarly journals Influence of Swell Wave on Wind Speed Retrieval Using ENVISAT ASAR Wave Mode Imagery

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Duo Wang ◽  
Xiaochen Wang ◽  
Weili Jiao
Keyword(s):  
Wind Speed ◽  
Incidence Angle ◽  
Weather Forecast ◽  
Wave Mode ◽  
Medium Range Weather Forecast ◽  
Envisat Asar ◽  
Main Work ◽  
Sar Imagery ◽  
The Relationship ◽  
Skewness And Kurtosis

The main work of this paper is to explore the influence of swell wave on retrieval of wind speed using ENVISAT ASAR wave mode imagery. The normalized radar cross section (NRCS) scene under different sea states is simulated to investigate the relationship between NRCS variation with swell height, together with swell direction. Moreover, the key parameter of imagery variance (Cvar) is selected to describe the swell wave on SAR imagery. In addition, the imagery parameters of skewness and kurtosis are together analyzed as a function of collocated significant swell wave height and wind speed. Based on the analyzed results, a new method for wind speed retrieval is proposed using ENVISAT ASAR, namely, F(n). Besides the CMOD parameters of NRCS, incidence angle, and relative wind direction, the imagery parameters of Cvar, skewness, and kurtosis are used to compensate for the influence of swell wave on wind speed retrieval in F(n). Finally, the collocated European Centre for Medium-Range Weather Forecast (ECMWF) wind speed dataset and ENVISAT ASAR wave mode imagery are used to verify the retrieval precision and compare with CMOD functions. It is concluded that the F(n) model performs much better than other CMOD functions, with a correlation of 0.89, a bias of 0.08, a RMSE of 1.2 m/s, and an SI of 0.1.

Telomeric repeats of Tetrahymena malaccensis mitochondrial DNA: a multimodal distribution that fluctuates erratically during growth

1988 ◽  
Vol 8 (10) ◽  
pp. 4450-4458
Author(s):  
G B Morin ◽  
T R Cech
Keyword(s):  
Mitochondrial Dna ◽  
Telomeric Repeats ◽  
Multimodal Distribution ◽  
Satellite Dnas ◽  
Multimodal Distributions ◽  
End Groups ◽  
Mean Size ◽  
The Mean ◽  
Average Size ◽  
End Group

The linear mitochondrial DNA (mtDNA) of Tetrahymena malaccensis has tandem 52-base-pair repeats at its telomeres. The mtDNA has a multimodal distribution of telomeres. Different groups in the distribution have different numbers of telomeric repeats. The standard deviation of the size of each end group is independent of the mean size of the end group. The two sides of the mtDNA have different multimodal distributions of repeats. Cloned cell lines have multimodal distributions of mtDNA telomeres distinct from that of the original cell line. The number of telomere end groups and the average size of the end groups change in an erratic fashion as the cells are passaged and do not reach a stable equilibrium distribution in 185 generations. We propose that the mean size of a telomere end group and the size distribution of an end group are independently regulated. The system controlling the average size of end groups may be defective in T. malaccensis, since a closely related species (T. thermophila) does not have a multimodal distribution of mtDNA telomeres. T. hyperangularis, which has different telomeric repeats on each side of its mtDNA, has a multimodal distribution of mtDNA telomeres on only one side, suggesting that the mechanism controlling the average number of repeats in an end group can be sequence specific. These mitochondrial telomeres provide a new example of the more general phenomenon of expansion and contraction of arrays of repeated sequences seen, for example, with simple-sequence "satellite" DNAs; however, the mitochondrial telomeres change on a very short time scale.

scholarly journals Analysis of approximations of GUM supplement 2 based non-Gaussian PDFs of measurement models with Rosenblatt Gaussian transformation mappings

2020 ◽  
Vol 11 ◽  
pp. 2
Author(s):  
Vishal Ramnath
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Random Variables ◽  
Measurement Model ◽  
Linear Measurement ◽  
Statistical Simulation ◽  
Implicit Assumption ◽  
Measurement Models ◽  
Gaussian System ◽  
Non Gaussian

In scientific metrology practise the application of Monte Carlo simulations with the aid of the GUM Supplement 2 (GS2) technique for performing multivariate uncertainty analyses is now more prevalent, however a key remaining challenge for metrologists in many laboratories is the implicit assumption of Gaussian characteristics for summarizing and analysing measurement model results. Whilst non-Gaussian probability density functions (PDFs) may result from Monte Carlo simulations when the GS2 is applied for more complex non-linear measurement models, in practice results are typically only reported in terms of multivariate expected and covariance values. Due to this limitation the measurement model PDF summary is implicitly restricted to a multivariate Gaussian PDF in the absence of additional higher order statistics (HOS) information. In this paper an earlier classical theoretical result by Rosenblatt that allows for an arbitrary multivariate joint distribution function to be transformed into an equivalent system of Gaussian distributions with mapped variables is revisited. Numerical simulations are performed in order to analyse and compare the accuracy of the equivalent Gaussian system of mapped random variables for approximating a measurement model’s PDF with that of an exact non-Gaussian PDF that is obtained with a GS2 Monte Carlo statistical simulation. Results obtained from the investigation indicate that a Rosenblatt transformation offers a convenient mechanism to utilize just the joint PDF obtained from the GS2 data in order to both sample points from a non-Gaussian distribution, and also in addition which allows for a simple two-dimensional approach to estimate coupled uncertainties of random variables residing in higher dimensions using conditional densities without the need for determining parametric based copulas.

The inverse transformation of the explicit fourth-moment standardization for structural reliability

2017 ◽  
Vol 21 (5) ◽  
pp. 769-782 ◽  
Author(s):  
Xuan-Yi Zhang ◽  
Yan-Gang Zhao ◽  
Zhao-Hui Lu
Keyword(s):  
Structural Reliability ◽  
Probability Distributions ◽  
Reliability Assessment ◽  
Random Variables ◽  
Inverse Transformation ◽  
Fourth Moment ◽  
Unknown Probability ◽  
Practical Engineering ◽  
Definition Of ◽  
Skewness And Kurtosis

In practical engineering, the probability distributions of some random variables are often unknown, and the only available information about these may be their statistical moments. To conduct structural reliability assessment without the exclusion of random variables with unknown probability distributions, an explicit fourth-moment standardization function has been proposed, and a single expression of its inverse transformation, that is, normal transformation, with limitations of inputting sets of the third and fourth moments (skewness and kurtosis) of random variables was derived. However, the clear definition of the complete expressions of the inverse transformation of fourth-moment standardization function under different combinations of skewness and kurtosis of random variables has not been provided yet. It is in this regard that four criteria are proposed to derive the complete inverse transformation of fourth-moment standardization function, and then the complete expressions of the inverse transformation are formulated. Through the numerical examples presented, the proposed complete expressions are found to be quite efficient for normal transformations and to be sufficiently accurate to include random variables with unknown probability distributions in structural reliability assessment.

Normal distribution of ventricular pressure-volume area of arrhythmic beats under atrial fibrillation in canine heart

2005 ◽  
Vol 288 (4) ◽  
pp. H1740-H1746 ◽  
Author(s):  
Satoshi Mohri ◽  
Juichiro Shimizu ◽  
Gentaro Iribe ◽  
Haruo Ito ◽  
Terumasa Morita ◽  
...  
Keyword(s):  
Atrial Fibrillation ◽  
Normal Distribution ◽  
Frequency Distribution ◽  
Mechanical Energy ◽  
Systolic Pressure ◽  
Left Ventricular ◽  
Canine Heart ◽  
Significance Level ◽  
Nonnormal Distribution ◽  
Skewness And Kurtosis

We previously found the frequency distribution of the left ventricular (LV) effective afterload elastance (Ea) of arrhythmic beats to be nonnormal or non-Gaussian in contrast to the normal distribution of the LV end-systolic elastance (Emax) in canine in situ LVs during electrically induced atrial fibrillation (AF). These two mechanical variables determine the total mechanical energy [systolic pressure-volume area (PVA)] generated by LV contraction when the LV end-diastolic volume is given on a per-beat basis. PVA and Emax are the two key determinants of the LV O2 consumption per beat. In the present study, we analyzed the frequency distribution of PVA during AF by its χ2, significance level, skewness, and kurtosis and compared them with those of other major cardiodynamic variables including Ea and Emax. We assumed the volume intercept (V0) of the end-systolic pressure-volume relation needed for Emax determination to be stable during arrhythmia. We found that PVA distributed much more normally than Ea and slightly more so than Emax during AF. We compared the χ2, significance level, skewness, and kurtosis of all the complex terms of the PVA formula. We found that the complexity of the PVA formula attenuated the effect of the considerably nonnormal distribution of Ea on the distribution of PVA along the central limit theorem. We conclude that mean (SD) of PVA can reliably characterize the distribution of PVA of arrhythmic beats during AF, at least in canine hearts.

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