China
Africa
Explore chapters and articles related to this topic
Basics of probability and statistics
Published in Amit Kumar Gorai, Snehamoy Chatterjee, Optimization Techniques and their Applications to Mine Systems, 2023
Amit Kumar Gorai, Snehamoy Chatterjee
The probability distribution for a discrete random variable is referred to as the probability mass function (PMF); whereas, the same is referred to as probability density function (PDF) for the continuous random variable. A PMF, P(X) or PDF, f(x) must be non-negative, and the sum of the probability of the entire sample space must be equal to 1. The probability distribution can be represented by a discrete or continuous function, as explained in subsequent subsections.
Demand and leakage management
Published in Bogumil Ulanicki, Kalanithy Vairavamoorthy, David Butler, Peter L.M. Bounds, Fayyaz Ali Memon, Water Management Challenges in Global Change, 2020
Bogumil Ulanicki, Kalanithy Vairavamoorthy, David Butler, Peter L.M. Bounds, Fayyaz Ali Memon
Time series predictors generally have no inbuilt mechanism for subsequent classification. One measure of abnormality using time series prediction is the ratio of observed vs. predicted values, with sustained deviation indicating a burst or other abnormal flow. Once trained the MDN predicts the conditional probability density function of the target data for any given value of the input vector, rather than just a point prediction, which is the case for most other ANN models used for time series prediction. The area under a probability density function curve equates to probability. The mixture model previously discussed is a linear combination of component densities (general normal distributions). A confidence interval for the predicted value (specified by the user) is computed from the mixture model.
Wind Speed Probability Distribution
Published in Yeqiao Wang, Atmosphere and Climate, 2020
Different moments carry information about different aspects of wind variability. The mean and standard deviation are measures of magnitude: they represent respectively the overall magnitude of the wind speed and the strength of the variability around it. In contrast, the skewness is a measure of the shape of the distribution. A skewness value of zero indicates that the pdf is symmetric around its mean, so anomalies (relative to the mean) of equal size and opposite sign are equally likely. A positive skewness indicates that positive anomalies of a given size are more likely than negative values of the same magnitude; for negative skewness, the asymmetry favors negative anomalies. Other measures of shape exist, such as kurtosis (a measure of the flatness of the distribution); as these are more sensitive to sampling variability than lower-order moments, they are less often used in practical applications.111 As noted earlier, the moments of w enter into the calculation of mean wind power density n: assuming a constant air density p,
High-speed train suspension health monitoring using computational dynamics and acceleration measurements
Published in Vehicle System Dynamics, 2020
David Lebel, Christian Soize, Christine Funfschilling, Guillaume Perrin
First, the values of parameters of interest that must be identified are uncertain by definition. Each parameter is thus represented by a random variable associated. Its prior probability density function (PDF) represents the initial knowledge available about this random variable, which may be deduced from specifications, tests or experts judgements. In the present case, because of the lack of initial knowledge about the parameters, the prior PDFs are chosen as uniform distributions on the parameters admissible intervals. It is assumed that the random variables that model the parameters are independent for the prior model and will be a priori dependent for the posterior one. The goal of Bayesian calibration is to update the prior PDF to determine the posterior PDF that takes into account the information provided by the experimental data. The parameters of interest are gathered in the random vector . The prior and posterior PDF of are respectively denoted as and . The support of is the set that is the set product of the parameters admissible intervals.
Probability distribution functions of turbulence using multiple criteria over non-uniform sand bed channel
Published in ISH Journal of Hydraulic Engineering, 2020
Probability density function (PDFs) of a random variable is a function that defines the relative possibility for the random variable to deal with a given value. Probability distribution function can be represented by Gaussian distribution, Log normal distribution, and many other etc. These distributions are based on the interval over which the convergence is finite. The advantage of Gram Charlier (GC) series to other series is that it is applicable to series containing interval over which the application of convergence is infinite (Cramer 1999). Also PDFs of GC series is developed considering the higher order moments up to four. The knowledge of PDF of turbulent parameters such as velocity fluctuation and Reynolds shear stress helps to understand the related turbulent parameters (Afzal et al. 2009; Van Atta and Chen 1968).
Waves plus currents crossing at a right angle: near-bed velocity statistics
Published in Journal of Hydraulic Research, 2018
C. Faraci, P. Scandura, R.E. Musumeci, E. Foti
In Fig. 16 the skewness and the flatness factors of the current velocity are shown versus the bottom distance, made non-dimensional by means of the water depth D. The skewness is a measure of the asymmetry of the probability density function with respect to the average value . For symmetric distributions with respect to , the skewness vanishes; an example of this behaviour is represented by the normal distribution. When the skewness is negative the largest fluctuations of are negative; the opposite occurs if the skewness is positive. The flatness provides a measure of the peakedness of the probability density function. In particular, the flatness is equal to 3 in the case of a normal distribution. In the present analysis, in the current only case the skewness has small values very close to the bed, then it decreases reaching values of −0.3 to −0.4 far from the bed. The flatness assumes values close to 3 near the bed, then it falls below 3 for and finally it increases, attaining values of about 3.5. These results show that a region close to the bottom exists where the skewness is small and the flatness is close to 3, thus explaining why in Fig. 13 the frequency distribution is well described by a Gaussian distribution.