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Continuous probability distributions
Published in Andrew Metcalfe, David Green, Tony Greenfield, Mahayaudin Mansor, Andrew Smith, Jonathan Tuke, Statistics in Engineering, 2019
Andrew Metcalfe, David Green, Tony Greenfield, Mahayaudin Mansor, Andrew Smith, Jonathan Tuke
A half normal distribution is obtained by folding a normal distribution with mean 0 about a vertical line through 0. It is a plausible model for run-out of circular components such as brake discs, CDs, and bicycle wheels. The pdf is f(x)=2σπe−x2/(2σ2)forx≥0.
Data-driven model-based flow measurement uncertainty quantification for building central cooling systems using a probabilistic approach
Published in Science and Technology for the Built Environment, 2023
Shaobo Sun, Kui Shan, Shengwei Wang
It is of vital importance to assign an appropriate prior distribution to each of the parameter to be quantified, i.e., the systematic and random uncertainties of flow measurements. The prior distributions can be generally derived from expert knowledge, experiments, surveys and industrial standards, etc. (Heo, Choudhary, and Augenbroe 2012). The prior distributions of systematic and random uncertainties are shown in Figure 6. In this study, the prior distribution of systematic uncertainty is normal and assigned based on a hypothesis. It assumes that the probability of the systematic uncertainty being less than 10% of the designed chilled water flow rate is 95%. As shown in Figure 6(a), the mean and standard deviation of the prior distribution are 0 and 1.99 respectively. The standard deviation of random uncertainty must be non-negative. The half-normal distribution () is used as its prior distribution, as shown in Figure 6(b).
Some Inferential Results on a Two Parameter Generalized Half Normal Distribution
Published in American Journal of Mathematical and Management Sciences, 2022
A random variable X is said to have a two-parameter Generalized Half Normal Distribution (henceforth ‘2 P-GHND’) provided its pdf is given as where x > 0, and The model parameters δ and σ are called the shape and scale parameters, respectively. The cdf of (1) is given as where represents the cdf of the standard normal distribution. It is easy to see that δ = 1 implies the half normal distribution with scale parameter σ, i.e., it is the folded distribution at zero on the positive side of the real line obtained from distribution. For any integer the kth raw moment of 2 P-GHND has the following expression where represents the usual gamma function evaluated at c. The model mean E(X) is denoted by η.
A scalable and practical method for disaggregating heating and cooling electrical usage using smart thermostat and smart metre data
Published in Journal of Building Performance Simulation, 2022
Sang woo Ham, Panagiota Karava, Ilias Bilionis, James Braun
The normalized net power () of a residential unit during discrete time () is modelled as a truncated normal distribution (Salvatier, Wiecki, and Fonnesbeck 2016) because it is a positive distribution: where is averaged net power during divided by its maximum value () so that the normalized data () are in a range [0,1]. and are the mean and standard deviation of the half-normal distribution. Normalized data and their parameters are marked with superscript *.