Improving daily rainfall extremes simulation using the generalized Pareto distribution: a case study in Western Iran

Prediction of the occurrence or non-occurrence of daily rainfall plays a significant role in agricultural planning and water resource management projects. In this study, gamma distribution function (GDF), kernel, and exponential (EXP) distributions were coupled (piecewise) with a generalized Pareto distribution. Thus, the gamma-generalized Pareto (GGP), kernel-generalized Pareto (KGP), and exponential-generalized Pareto (EGP) models were used. The aim of the present study was to introduce new methods to modify the simulated generation of extreme rainfall amounts of rainy seasons based on the preserved spatial correlation. The best approach was identified using the normalized root mean square error (NRMSE) criterion. For this purpose, the 30-yr daily rainfall datasets of 21 synoptic weather stations located in different climates of West Iran were analyzed. The first, second, and third-order Markov chain (MC) models were used to describe rainfall time series frequencies. The best MC model order was detected using the Akaike information criterion and Bayesian information criterion. Based on the best identified MC model order, the best piecewise distribution models, and the Wilks approach, rainfall events were modeled with regard to the spatial correlation among the study stations. The performance of the Wilks approach was verified using the coefficient of determination. The daily rainfall simulation resulted in a good agreement between the observed and the generated rainfall data. Hence, the proposed approach is capable of helping water resource managers in different contexts of agricultural planning.

On the Properties of the New Generalized Pareto Distribution and Its Applications

In this paper, a new generalization of the Generalized Pareto distribution is proposed using the generator suggested in [1], named as Khalil Extended Generalized Pareto (KEGP) distribution. Various shapes of the suggested model and important mathematical properties are investigated that includes moments, quantile function, moment-generating function, measures of entropy, and order statistics. Parametric estimation of the model is discussed using the technique of maximum likelihood. A simulation study is performed for the assessment of the maximum likelihood estimates in terms of their bias and mean squared error using simulated sample estimates. The practical applications are illustrated via two real data sets from survival and reliability theory. The suggested model provided better fits than the other considered models.

Inferences for Generalized Pareto Distribution Based on Progressive First-Failure Censoring Scheme

In this article, we consider estimation of the parameters of a generalized Pareto distribution and some lifetime indices such as those relating to reliability and hazard rate functions when the failure data are progressive first-failure censored. Both classical and Bayesian techniques are obtained. In the Bayesian framework, the point estimations of unknown parameters under both symmetric and asymmetric loss functions are discussed, after having been estimated using the conjugate gamma and discrete priors for the shape and scale parameters, respectively. In addition, both exact and approximate confidence intervals as well as the exact confidence region for the estimators are constructed. A practical example using a simulated data set is analyzed. Finally, the performance of Bayes estimates is compared with that of maximum likelihood estimates through a Monte Carlo simulation study.

Performance-based comparison of regionalization methods to improve the at-site estimates of daily precipitation

In this article, we compare the performances of three regionalization approaches in improving the at-site estimates of daily precipitation. The first method is built on the idea of conventional RFA (Regional Frequency Analysis) but is based on a fast algorithm that defines distinct homogeneous regions relying on their upper tail similarity. It uses only the precipitation data at hand without the need for any additional covariate. The second is based on the region-of-influence (ROI) approach in which neighborhoods, containing similar sites, are defined for each station. The third is a spatial method that adopts Generalized Additive Model (GAM) forms for the model parameters. In line with our goal of modeling the whole range of positive precipitation, the chosen marginal distribution model is the Extended Generalized Pareto Distribution (EGPD) on which we apply the three methods. We consider a dense network composed of 1176 daily stations located within Switzerland and in neighboring countries. We compute different criteria to assess the models' performances both in the bulk of the distribution as well as in the upper tail. The results show that all the regional methods offered improved robustness over the local EGPD model. While the GAM method is more robust and reliable in the upper tail, the ROI method is better in the bulk of the distribution.

Uncertainty analysis of strong earthquake hazard estimation based on the generalized Pareto distribution model: A case study of the northeastern Tibetan Plateau

A statistical method to analyze the uncertainties of strong earthquake hazard estimation is proposed from Generalized Pareto distribution (GPD) model using the northeastern Tibetan Plateau earthquake catalogue (1885–2017) data. For magnitude threshold of 5.5, the magnitude return levels in 20, 50, 100, 200, and 500 years are 7.19, 7.70, 7.99, 8.22, and 8.45, respectively. The corresponding 95% confidence intervals are [6.77, 7.60], [7.27, 8.12], [7.53, 8.44], [7.71, 8.72], and [7.84, 9.06], respectively. The upper magnitude limit obtained from this GPD model is 9.07 and its 80% confidence interval is [8.16, 9.98]. The sensitivity analysis by the Morris method indicates that the input magnitude threshold has a relatively large influence on the estimation results. Thus, threshold selection is important for the GPD model construction. The sensitivity characteristic ranking of input factors become increasingly stable with the increasing of return period, which implies that GPD model is more suitable for estimating strong earthquakes magnitude return levels and upper magnitude limit. The GPD modeling approach and qualitative uncertainty analysis methods for strong earthquake hazard estimations proposed in this paper can be applied to seismic hazard analysis elsewhere.

Estimation of aggregate losses of secondary cancer cases using PH Panjer class (a,b,1) distributions,

This research in-cooperates phase type distributions of Panjer class \((a,b,1)\) in estimation of aggregate loss probabilities of secondary cancer. Matrices of the phase type distributions are derived using Chapman-Kolmogorov equation and transition probabilities estimated using modified Kaplan-Meir and consequently the transition intensities and transition probabilities. Stationary probabilities of the Markov chains represents $\vec{\gamma}$. Claim amount are modeled using OPPL, TPPL, Pareto, Generalized Pareto and Wei-bull distributions. PH ZT Poisson with Generalized Pareto distribution provided the best fit.

Automatic Superpixel-Based Clustering for Color Image Segmentation Using q-Generalized Pareto Distribution under Linear Normalization and Hunger Games Search

Superixel is one of the most efficient of the image segmentation approaches that are widely used for different applications. In this paper, we developed an image segmentation based on superpixel and an automatic clustering using q-Generalized Pareto distribution under linear normalization (q-GPDL), called ASCQPHGS. The proposed method uses the superpixel algorithm to segment the given image, then the Density Peaks clustering (DPC) is employed to the results obtained from the superpixel algorithm to produce a decision graph. The Hunger games search (HGS) algorithm is employed as a clustering method to segment the image. The proposed method is evaluated using two different datasets, collected form Berkeley segmentation dataset and benchmark (BSDS500) and standford background dataset (SBD). More so, the proposed method is compared to several methods to verify its performance and efficiency. Overall, the proposed method showed significant performance and it outperformed all compared methods using well-known performance metrics.

Statistical properties of the aftershocks of stock market crashes revisited: Analysis based on the 1987 crash, financial-crisis-2008 and COVID-19 pandemic

During any unique crisis, panic sell-off leads to a massive stock market crash that may continue for more than a day, termed as mainshock. The effect of a mainshock in the form of aftershocks can be felt throughout the recovery phase of stock price. As the market remains in stress during recovery, any small perturbation leads to a relatively smaller aftershock. The duration of the recovery phase has been estimated using structural break analysis. We have carried out statistical analyses of 1987 stock market crash, 2008 financial crisis and 2020 COVID-19 pandemic considering the actual crash times of the mainshock and aftershocks. Earlier, such analyses were done considering absolute one-day return, which cannot capture a crash properly. The results show that the mainshock and aftershock in the stock market follow the Gutenberg–Richter (GR) power law. Further, we obtained higher [Formula: see text] value for the COVID-19 crash compared to the financial-crisis-2008 from the GR law. This implies that the recovery of stock price during COVID-19 may be faster than the financial-crisis-2008. The result is consistent with the present recovery of the market from the COVID-19 pandemic. The analysis shows that the high-magnitude aftershocks are rare, and low-magnitude aftershocks are frequent during the recovery phase. The analysis also shows that the inter-occurrence times of the aftershocks follow the generalized Pareto distribution, i.e. [Formula: see text], where [Formula: see text] and [Formula: see text] are constants and [Formula: see text] is the inter-occurrence time. This analysis may help investors to restructure their portfolio during a market crash.

Intensity and frequency of extreme novel epidemics

Observational knowledge of the epidemic intensity, defined as the number of deaths divided by global population and epidemic duration, and of the rate of emergence of infectious disease outbreaks is necessary to test theory and models and to inform public health risk assessment by quantifying the probability of extreme pandemics such as COVID-19. Despite its significance, assembling and analyzing a comprehensive global historical record spanning a variety of diseases remains an unexplored task. A global dataset of historical epidemics from 1600 to present is here compiled and examined using novel statistical methods to estimate the yearly probability of occurrence of extreme epidemics. Historical observations covering four orders of magnitude of epidemic intensity follow a common probability distribution with a slowly decaying power-law tail (generalized Pareto distribution, asymptotic exponent = −0.71). The yearly number of epidemics varies ninefold and shows systematic trends. Yearly occurrence probabilities of extreme epidemics, Py, vary widely: Py of an event with the intensity of the “Spanish influenza” (1918 to 1920) varies between 0.27 and 1.9% from 1600 to present, while its mean recurrence time today is 400 y (95% CI: 332 to 489 y). The slow decay of probability with epidemic intensity implies that extreme epidemics are relatively likely, a property previously undetected due to short observational records and stationary analysis methods. Using recent estimates of the rate of increase in disease emergence from zoonotic reservoirs associated with environmental change, we estimate that the yearly probability of occurrence of extreme epidemics can increase up to threefold in the coming decades.