scholarly journals Tuning the Bivariate Meta-Gaussian Distribution Conditionally in Quantifying Precipitation Prediction Uncertainty

Forecasting ◽  
2020 ◽  
Vol 2 (1) ◽  
pp. 1-19 ◽  
Author(s):  
Limin Wu
Keyword(s):  
Gaussian Distribution ◽  
Conditional Distribution ◽  
Joint Distribution ◽  
Goodness Of Fit ◽  
Pearson Correlation ◽  
Parameter Tuning ◽  
Bivariate Distribution ◽  
Distribution Model ◽  
Standard Normal ◽  
Forecast Variable

One of the ways to quantify uncertainty of deterministic forecasts is to construct a joint distribution between the forecast variable and the observed variable; then, the uncertainty of the forecast can be represented by the conditional distribution of the observed given the forecast. The joint distribution of two continuous hydrometeorological variables can often be modeled by the bivariate meta-Gaussian distribution (BMGD). The BMGD can be obtained by transforming each of the two variables to a standard normal variable and the dependence between the transformed variables is provided by the Pearson correlation coefficient of these two variables. The BMGD modeling is exact provided that the transformed joint distribution is standard normal. In real-world applications, however, this normality assumption is hardly fulfilled. This is often the case for the modeling problem we consider in this paper: establish the joint distribution of a forecast variable and its corresponding observed variable for precipitation amounts accumulated over a duration of 24 h. In this case, the BMGD can only serve as an approximate model and the dependence parameter can be estimated in a variety of ways. In this paper, the effect of tuning this parameter is studied. Numerical simulations conducted suggest that, while the parameter tuning results in limited improvements in goodness-of-fit (GOF) for the BMGD as a bivariate distribution model, better results may be achieved by tuning the parameter for the one-dimensional conditional distribution of the observed given the forecast greater than a certain large value.

scholarly journals Mathematical pattern of Kessler psychological distress distribution in the general population of the U.S. and Japan

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Shinichiro Tomitaka ◽  
Toshiaki A. Furukawa
Keyword(s):  
United States ◽  
General Population ◽  
National Survey ◽  
Goodness Of Fit ◽  
Quadratic Function ◽  
The United States ◽  
Depression Screening ◽  
Distribution Model ◽  
Epidemiological Surveys ◽  
Screening Scale

Abstract Background Although the 6-item Kessler psychological scale (K6) is a useful depression screening scale in clinical settings and epidemiological surveys, little is known about the distribution model of the K6 score in the general population. Using four major national survey datasets from the United States and Japan, we explored the mathematical pattern of the K6 distributions in the general population. Methods We analyzed four datasets from the National Health Interview Survey, the National Survey on Drug Use and Health, and the Behavioral Risk Factor Surveillance System in the United States, and the Comprehensive Survey of Living Conditions in Japan. We compared the goodness of fit between three models: exponential, power law, and quadratic function models. Graphical and regression analyses were employed to investigate the mathematical patterns of the K6 distributions. Results The exponential function had the best fit among the three models. The K6 distributions exhibited an exponential pattern, except for the lower end of the distribution across the four surveys. The rate parameter of the K6 distributions was similar across all surveys. Conclusions Our results suggest that, regardless of different sample populations and methodologies, the K6 scores exhibit a common mathematical distribution in the general population. Our findings will contribute to the development of the distribution model for such a depression screening scale.

scholarly journals A general stochastic model for bivariate episodes driven by a gamma sequence

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Charles K. Amponsah ◽  
Tomasz J. Kozubowski ◽  
Anna K. Panorska
Keyword(s):  
Stochastic Model ◽  
Joint Distribution ◽  
Pareto Distribution ◽  
Integral Transforms ◽  
Bivariate Distribution ◽  
Conditional Distributions ◽  
General Stochastic Model ◽  
Heavy Tailed ◽  
Discrete Pareto Distribution ◽  
Special Case

AbstractWe propose a new stochastic model describing the joint distribution of (X,N), where N is a counting variable while X is the sum of N independent gamma random variables. We present the main properties of this general model, which include marginal and conditional distributions, integral transforms, moments and parameter estimation. We also discuss in more detail a special case where N has a heavy tailed discrete Pareto distribution. An example from finance illustrates the modeling potential of this new mixed bivariate distribution.

Evaluation of the Hourly Global Solar Radiation on a Horizontal Plane for Two Sites in Algeria

2014 ◽  
Vol 925 ◽  
pp. 641-645 ◽  
Author(s):  
Mohamed Salmi ◽  
Hassen Bouzgou ◽  
Yarub Al-Douri ◽  
Abdelhakim Boursas
Keyword(s):  
Solar Radiation ◽  
Gaussian Distribution ◽  
Horizontal Plane ◽  
Experimental Validation ◽  
Global Solar Radiation ◽  
Distribution Model ◽  
Experimental Assessment ◽  
Precise Prediction ◽  
Gaussian Distribution Model ◽  
Modelling Approach

We present three models for the estimation of hourly global solar radiation for two sites in Algeria, namely: Djelfa (Latitude 34.68°N, Longitude 3.25°E, Altitude 1126 (m)) and Ain Bessem (Latitude 36.31°N, Longitude 3.67°E, Altitude 629 (m)). The models are: the Gaussian distribution model, the model by Collares-Pereira-RabI and the H.A. model (Hourly absolute modelling approach). The experimental assessment was done using recorded values of the hourly global solar radiation on a horizontal plane during the period 2000-2004. The obtained results show a close similarity between the solar radiation values calculated by the three models and the measured values, especially for the first model. The experimental validation shows promising results for the estimation and precise prediction of the hourly global solar radiation.

Remaining Useful Life Estimation Based on a Segmental Hidden Markov Model With Continuous Observations

2017 ◽  
Author(s):  
Zhen Chen ◽  
Tangbin Xia ◽  
Ershun Pan
Keyword(s):  
Markov Model ◽  
Hidden Markov Model ◽  
Goodness Of Fit ◽  
Hidden Markov ◽  
Remaining Useful Life ◽  
Likelihood Method ◽  
Distribution Model ◽  
Unknown Parameters ◽  
Useful Life ◽  
Hidden States

In this paper, a segmental hidden Markov model (SHMM) with continuous observations, is developed to tackle the problem of remaining useful life (RUL) estimation. The proposed approach has the advantage of predicting the RUL and detecting the degradation states simultaneously. As the observation space is discretized into N segments corresponding to N hidden states, the explicit relationship between actual degradation paths and the hidden states can be depicted. The continuous observations are fitted by Gaussian, Gamma and Lognormal distribution, respectively. To select a more suitable distribution, model validation metrics are employed for evaluating the goodness-of-fit of the available models to the observed data. The unknown parameters of the SHMM can be estimated by the maximum likelihood method with the complete data. Then a recursive method is used for RUL estimation. Finally, an illustrate case is analyzed to demonstrate the accuracy and efficiency of the proposed method. The result also suggests that SHMM with observation probability distribution which is closer to the real data behavior may be more suitable for the prediction of RUL.

scholarly journals Sensitivity study of ring-shaped electrostatic sensor based on nonparametric estimation

2021 ◽  
Vol 2121 (1) ◽  
pp. 012019
Author(s):  
Zhe Kan ◽  
Yuanzhe Li
Keyword(s):  
Gaussian Distribution ◽  
Relative Permittivity ◽  
Goodness Of Fit ◽  
Estimation Method ◽  
Kernel Estimation ◽  
Sensitivity Study ◽  
Simulation Software ◽  
Spatial Sensitivity ◽  
Theoretical Sensitivity ◽  
Induction Model

Abstract In this paper, aiming at the problem of the electrostatic sensor signal satisfying the gaussian distribution, the non-parametric kernel estimation method is introduced, and the electrode induction model of the electrostatic sensor is finally fitted by combining the goodness of fit and the simulation data samples. This model satisfies the gaussian distribution and the electrostatic signal satisfying the gaussian distribution is given in the theory. Maxwell simulation software was used to simulate the theoretical sensitivity of the electrostatic sensor and the axial and radial spatial sensitivity characteristics of different sensor parameters were obtained. Within a certain range, the relative permittivity of the insulating tube is also discussed. Finally, an insulating tube with a relative permittivity of 3 is selected as the material of the insulating tube. Finally, the experiment is carried out on the experimental equipment and the conclusions obtained in the article are confirmed.

scholarly journals On a characterization theorem on a-adic solenoids

2019 ◽  
Vol 489 (3) ◽  
pp. 227-231
Author(s):  
G. M. Feldman
Keyword(s):  
Gaussian Distribution ◽  
Real Line ◽  
Linear Form ◽  
Conditional Distribution ◽  
Random Variables ◽  
Characterization Theorem ◽  
The Other ◽  
Independent Random Variables ◽  
Linear Forms ◽  
The Real

According to the Heyde theorem the Gaussian distribution on the real line is characterized by the symmetry of the conditional distribution of one linear form of independent random variables given the other. We prove an analogue of this theorem for linear forms of two independent random variables taking values in an -adic solenoid containing no elements of order 2. Coefficients of the linear forms are topological automorphisms of the -adic solenoid.

Sign in / Sign up

Export Citation Format

Share Document