scholarly journals A Phenomenological Epidemic Model Based On the Spatio-Temporal Evolution of a Gaussian Probability Density Function

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2000
Author(s):  
Domingo Benítez ◽  
Gustavo Montero ◽  
Eduardo Rodríguez ◽  
David Greiner ◽  
Albert Oliver ◽  
...  
Keyword(s):  
Standard Deviation ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Epidemic Model ◽  
Temporal Evolution ◽  
Growth Models ◽  
Model Fit ◽  
Gaussian Probability Density Function ◽  
Spatio Temporal

A novel phenomenological epidemic model is proposed to characterize the state of infectious diseases and predict their behaviors. This model is given by a new stochastic partial differential equation that is derived from foundations of statistical physics. The analytical solution of this equation describes the spatio-temporal evolution of a Gaussian probability density function. Our proposal can be applied to several epidemic variables such as infected, deaths, or admitted-to-the-Intensive Care Unit (ICU). To measure model performance, we quantify the error of the model fit to real time-series datasets and generate forecasts for all the phases of the COVID-19, Ebola, and Zika epidemics. All parameters and model uncertainties are numerically quantified. The new model is compared with other phenomenological models such as Logistic Grow, Original, and Generalized Richards Growth models. When the models are used to describe epidemic trajectories that register infected individuals, this comparison shows that the median RMSE error and standard deviation of the residuals of the new model fit to the data are lower than the best of these growing models by, on average, 19.6% and 35.7%, respectively. Using three forecasting experiments for the COVID-19 outbreak, the median RMSE error and standard deviation of residuals are improved by the performance of our model, on average by 31.0% and 27.9%, respectively, concerning the best performance of the growth models.

scholarly journals Comparison Of Three Numerical Methods For Estimating Weibull Parameters Using Weibull Distribution Model In Nigeria

2020 ◽  
Vol 27 (2) ◽  
pp. 8-15
Author(s):  
J.A. Oyewole ◽  
F.O. Aweda ◽  
D. Oni
Keyword(s):  
Standard Deviation ◽  
Wind Speed ◽  
Probability Density Function ◽  
Weibull Distribution ◽  
Probability Density ◽  
Density Function ◽  
Accurate Estimation ◽  
Weibull Parameters ◽  
Factor Method ◽  
Deviation Method

There is a crucial need in Nigeria to enhance the development of wind technology in order to boost our energy supply. Adequate knowledge about the wind speed distribution becomes very essential in the establishment of Wind Energy Conversion Systems (WECS). Weibull Probability Density Function (PDF) with two parameters is widely accepted and is commonly used for modelling, characterizing and predicting wind resource and wind power, as well as assessing optimum performance of WECS. Therefore, it is paramount to precisely estimate the scale and shape parameters for all regions or sites of interest. Here, wind data from year 2000 to 2010 for four different locations (Port Harcourt, Ikeja, Kano and Jos) were analysed and the Weibull parameters was determined. The three methods employed are Mean Standard Deviation Method (MSDM), Energy Pattern Factor Method (EPFM) and Method of Moments (MOM) for estimating Weibull parameters. The method that gave the most accurate estimation of the wind speed was MSDM method, while Energy Pattern Factor Method (EPFM) is the most reliable and consistent method for estimating probability density function of wind. Keywords: Weibull Distribution, Method of Moment, Mean Standard Deviation Method, Energy Pattern Method

Facts about the gaussian probability density function

1995 ◽  
Vol 59 (1-4) ◽  
pp. 289-306 ◽  
Author(s):  
B. Aldershof ◽  
J.S. Marron ◽  
B.U. Park ◽  
M.P. Wand
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Gaussian Probability Density Function

scholarly journals Evaluation of a Flexible Single Ice Microphysics and a Gaussian Probability-Density-Function Macrophysics Scheme in a Single Column Model

Atmosphere ◽  
2021 ◽  
Vol 12 (5) ◽  
pp. 638
Author(s):  
Jiabo Li ◽  
Xindong Peng ◽  
Xiaohan Li ◽  
Yanluan Lin ◽  
Wenchao Chu
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Water Content ◽  
Density Function ◽  
Liquid Water ◽  
Cloud Fraction ◽  
Gaussian Probability Density Function ◽  
Single Column ◽  
Ice Water Content ◽  
Ice Water

Scale-aware parameterizations of subgrid scale physics are essentials for multiscale atmospheric modeling. A single-ice (SI) microphysics scheme and Gaussian probability-density-function (Gauss-PDF) macrophysics scheme were implemented in the single-column Global-to-Regional Integrated forecast System model (SGRIST) and they were tested using the Tropical Warm Pool-International Cloud Experiment (TWP-ICE) and the Atmospheric Radiation Measurement Southern Great Plains Experiment in 1997 (ARM97). Their performance was evaluated against observations and other reference schemes. The new schemes simulated reasonable precipitation with proper fluctuations and peaks, ice, and liquid water contents, especially in lower levels below 650 hPa during the wet period in the TWP-ICE. The root mean square error (RMSE) of the simulated cloud fraction was below 200 hPa was 0.10/0.08 in the wet/dry period, which showed an obvious improvement when compared to that, i.e., 0.11/0.11 of original scheme. Accumulated ice water content below the melting level decreased by 21.57% in the SI. The well-matched average liquid water content displayed between the new scheme and observations, which was two times larger than those with the referencing scheme. In the ARM97 simulations, the SI scheme produced considerable ice water content, especially when convection was active. Low-level cloud fraction and precipitation extremes were improved using the Gauss-PDF scheme, which displayed the RMSE of cloud fraction of 0.02, being only half of the original schemes. The study indicates that the SI and Gauss-PDF schemes are promising approaches to simplify the microphysics process and improve the low-level cloud modeling.

Understanding of Relationship Between the Average Mass Transport Rate And The Moments Of Permeability

1999 ◽  
Vol 556 ◽  
Author(s):  
Y. Niibori ◽  
O. Tochiyama ◽  
T. Chida
Keyword(s):  
Standard Deviation ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Measurement Data ◽  
Upper And Lower Bounds ◽  
Borehole Data ◽  
Average Mass ◽  
Permeability Distribution ◽  
Nuclide Transport

AbstractTo estimate the transport rate of radionuclides in the geosphere, we must consider the spatial variability of permeability. However, the borehole data of permeability are limited and we can not determine the type of probability density function, though the measurement data reflect the most significant hydraulic properties about geologic media including innumerable cracks or fast flow paths. While the recent models describing radioactive nuclide transport in near/far-field have assumed a certain probability density function (typically a lognormal distribution) as a permeability distribution, we cannot always obtain sufficient measurement data to define the function. However, the available data of permeability at least give us the moments such as the arithmetic mean, the standard deviation and the skewness for the distribution.The purpose of this paper is to get an understanding of the general relationship between the average mass transport rates and the moments. Using various types of probability density functions and pseudo random-numbers, hypothetical permeability distributions are generated. With these distributions, this paper obtains the average transport rates described as the numerical impulseresponse based on the advection-dispersion model for a two-dimensional region. The calculated results show that, for the dimensionless standard deviation up to around 1, the three moments are enough to characterize the permeability distribution for the purposes of the nuclide transport prediction.In this work, for five specified probability density functions, the upper and lower bounds of skewness are derived as a function of the dimensionless arithmetic mean and standard deviation. The obtained upper and lower bounds explicitly show that the Bernoulli trials (a discrete probability density function) yield the widest range in the skewness against the standard deviation. Since the response has lower peak and longer tail as the skewness goes to the lower bound value, we can predict the shape of the breakthrough curve from the three moments of the borehole data.

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