Statistical Inference of Dynamic Conditional Generalized Pareto Distribution with Weather and Air Quality Factors

Abstract

Air pollution is a major global problem, closely related to economic and social development and ecological environment construction. Air pollution data for most regions of China have a close correlation with time and seasons and are affected by multidimensional factors such as meteorology and air quality. In contrast with classical peaks-over-threshold modeling approaches, we use a deep learning technique and three new dynamic conditional generalized Pareto distribution (DCP) models with weather and air quality factors for fitting the time-dependence of the air pollutant concentration and make statistical inferences about their application in air quality analysis.Specifically, in the proposed three DCP models, a dynamic autoregressive exponential function mechanism is applied for the time-varying scale parameter and tail index of the conditional generalized Pareto distribution, and a sufficiently high threshold is chosen using two threshold selection procedures. The probabilistic properties of the DCP model and the statistical properties of the maximum likelihood estimation (MLE) are investigated, simulating and showing the stability and sensitivity of the MLE estimations. The three proposed models are applied to fit the PM2.5 time series in Beijing from 2015 to 2021. Real data are used to illustrate the advantages of the DCP, especially compared to the estimation volatility of GARCH and AIC or BIC criteria. The DCP model involving both the mixed weather and air quality factors performs better than the other two models with weather factors or air quality factors alone. Finally, a prediction modelbased on long short-term memory (LSTM) is used to predict PM2.5 concentration, achieving ideal results.

Generating Optimal Discrete Analogue of the Generalized Pareto Distribution under Bayesian Inference with Applications

“…These data comprise daily new deaths. The data are as follows: 52, 26, 36, 63, 52, 37,35,28,17,21,31,30,10,56,40,14,28,42,24,21,28,22,12,31,24,14,13,25,12,7,13,20,23,9,11,13,3,7,10,21,15,17,5,7,22,24,15,19,18,16,5,20,27. The data are available on the Worldometer website at [36].…”

“…Recently, many authors have studied the continuous GPD; for example, one may refer to [27], in which the authors discussed baseline methods for parameter estimation. The authors of [28] performed statistical inference of the dynamic conditional GPD with weather and air quality factors, and [29] discussed outlier-robust truncated maximum likelihood parameter estimators of the GPD. Reference [30] introduced risk analysis using the GPD.…”

On Statistical Inference of Generalized Pareto Distribution with Jointly Progressive Censored Samples with Binomial Removal

“…GP distribution has many applications and it can model many real life distributions, recently many authors studied GP distribution, for example, one may refer to Martín et al [15], who discussed baseline methods for the parameter estimation. Huang et al [16] obtained statistical inference of dynamic conditional GP distribution with weather and air quality factors. Shui et al [17] discussed outlier-robust truncated maximum likelihood parameter estimators of GP distribution.…”

From Multi- to Univariate: A Product Random Variable with an Application to Electricity Market Transactions: Pareto and Student’s t-Distribution Case

“…[12][13][14][15] for an application of the Student's t distribution and Refs. [16][17][18][19]-for the Pareto distribution. The Pareto distribution is skewed with power-law tails, while the Student's t distribution is symmetric and bell-shaped.…”