A new flexible Weibull extension model: Different estimation methods and modeling an extreme value data

ABSTRACTOften in practice one is interested in the situation where the lifetime data are censored. Censorship is a common phenomenon frequently encountered when analyzing lifetime data due to time constraints. In this paper, the flexible Weibull distribution proposed in Bebbington et al. [A flexible Weibull extension, Reliab. Eng. Syst. Safety 92 (2007), pp. 719–726] is studied using maximum likelihood technics based on three different algorithms: Newton Raphson, Levenberg Marquardt and Trust Region reflective. The proposed parameter estimation method is introduced and proved to work from theoretical and practical point of view. On one hand, we apply a maximum likelihood estimation method using complete simulated and real data. On the other hand, we study for the first time the model using simulated and real data for type I censored samples. The estimation results are approved by a statistical test.

The existence of nonmonotonic hazard rates was recognized from the study of human mortality three centuries ago. Among such hazard rates, ones with bathtub or upside-down bathtub shape have received considerable attention during the last five decades. Several models have been suggested to represent lifetimes possessing bathtub-shaped hazard rates. In this chapter, we review the existing results and also discuss some new models based on quantile functions. We discuss separately bathtub-shaped distributions with two parameters, three parameters, and then more flexible families. Among the two-parameter models, the Topp-Leone distribution, exponential power, lognormal, inverse Gaussian, Birnbaum and Saunders distributions, Dhillon’s model, beta, Haupt-Schabe models, loglogistic, Avinadev and Raz model, inverse Weibull, Chen’s model and a flexible Weibull extension are presented along with their quantile functions. The quadratic failure rate distribution, truncated normal, cubic exponential family, Hjorth model, generalized Weibull model of Mudholkar and Kollia, exponentiated Weibull, Marshall-Olkin family, generalized exponential, modified Weibull extension, modified Weibull, generalized power Weibull, logistic exponential, generalized linear failure rate distribution, generalized exponential power, upper truncated Weibull, geometric-exponential, Weibull-Poisson and transformed model are some of the distributions considered under three-parameter versions. Distributions with more than three parameters introduced by Murthy et al., Jiang et al., Xie and Lai, Phani, Agarwal and Kalla, Kalla, Gupta and Lvin, and Carrasco et al. are presented as more flexible families. We also introduce general methods that enable the construction of distributions with nonmonotone hazard functions. In the case of many of the models so far specified, the hazard quantile functions and their analysis are also presented to facilitate a quantile-based study. Finally, the properties of total time on test transforms and Parzen’s score function are utilized to develop some new methods of deriving quantile functions that have bathtub hazard quantile functions.

Problem setting. Artificial intelligence is rapidly affecting the financial sector with countless potential benefits in terms of improving financial services and compliance. In the financial sector, artificial intelligence algorithms are already trusted to account for transactions, detect fraudulent schemes, assess customer creditworthiness, resource planning and reporting. But the introduction of such technologies entails new risks. Analysis of resent researches and publications. The following scientists were engaged in research of the specified question: D.W. Arner, J. Barberis, R.P. Buckley, Jon Truby, Rafael Brown, Andrew Dahdal, O. A. Baranov, O. V. Vinnyk, I. V. Yakovyuk, A. P. Voloshin, A. O. Shovkun, N.B. Patsuriia. Target of research. The aim of the article is to identify key strategic issues in developing mechanisms to ensure the effective implementation and use of artificial intelligence in the financial services market. Article’s main body. The paper investigates an important scientific and practical problem of legal regulation of artificial intelligence used by financial services market participants. The legal risks associated with the use of artificial intelligence programs in a particular area are considered. The most pressing risks to address targeted AI regulation are fundamental rights, data confidentiality, security and effective performance, and accountability. This article argues that the best way to encourage a sustainable future in AI innovation in the financial sector is to support a proactive regulatory approach prior to any financial harm occurring. This article argues that it would be optimal for policymakers to intervene early with targeted, proactive but balanced regulatory approaches to AI technology in the financial sector that are consistent with emerging internationally accepted principles on AI governance. Conclusions and prospects for the development. The adoption of rational regulations that encourage innovation whilst ensuring adherence to international principles will significantly reduce the likelihood that AI-related risks will develop into systemic problems. Leaving the financial sector only with voluntary codes of practice may encourage experimentation that in turn may result in innovative benefits – but it will definitely render customers vulnerable, institutions exposed and the entire financial system weakened.

This paper is devoted to study a new mixture model. This newly suggested model is a mixture of flexible Weibull extension and Burr XII distributions. We study the characteristics of the proposed distribution that includes probability density function, cumulative distribution function, reliability function and ageing behaviour through the failure rate function. Some statistical properties of the proposed distribution such as quantile function, the mode, median, r-th moments, the moment generating function and the order statistics are discussed. Moreover, the method of maximum likelihood is proposed for estimating the model parameters and also the Fisher's information matrix is derived. Finally, the performance of the proposed distribution is compared with existing distributions using applications of two real data sets to show the flexibility and efficiency of the new model.

A stochastic flood model with a Weibull distribution for flood exceedances is examined and compared to the traditional exponential-based model in terms of predictive and descriptive properties. The model is based upon the traditional representation of the flood mechanism as a Poisson counting process. It is expected that the more flexible Weibull distribution will be capable of modeling flood series which exhibit a wider range of variability than the exponential model. The Weibull-based model is shown to possess predictive properties which are superior to the exponential model when samples exhibit coefficients of variation less than 1.5 and sample sizes are on the order of 2 events per year. These characteristics are shown to exist in many observed flood series in the Gulf Coast of the United States.

Here we consider how extreme events, particularly climatic and biotic, affect the physiology, development, ecology and evolution of organisms, focusing on plants. The marked effects on organisms are of increasing interest for ecological prediction, given the natural and anthropogenic changes in spectra of extreme events being induced by global change. Yet there is currently a paucity of knowledge or even a common world-view of how extreme events shape individuals, communities and ecosystems. We propose that extreme events need be defined in terms of organismal responses of acclimation and of de-acclimation or hysteresis. From this definition we proceed to develop a number of hypotheses, including that fitness effects of extreme events occur primarily during recovery. We review evidence that, on the evolutionary time scale, selection is virtually absent except during extreme events; these drive strong directional selection, even to trait fixation and speciation. We describe a number of new tools, both conceptual and technological, that are now at hand or that merit rapid development. Contents I. Introduction 22 II. Moving to an organismally based definition of extreme events 22 III. Features to discern in extreme events 26 IV. Additional challenges in the study of extreme events 27 V. Evolutionary dimensions 29 VI. The mandate for new conceptual tools for ecological and evolutionary prediction 34 VII. Tools in hand, and tools needed, to study extreme events 35 VIII. Conclusions 37 Acknowledgements 37 References 38.

In this article we introduce a new four - parameters model called the odd generalized exponential flexible Weibull extension (OGE-FWE) distribution which exhibits bathtub-shaped hazard rate. Some of it’s statistical properties are obtained including ordinary and incomplete moments, quantile and mode, the moment generating functions, reliability and order statistics. The method of maximum likelihood is used for estimating the model parameters and the observed Fisher’s information matrix is given. Moreover, we give the advantage of the OGE-FWE distribution by an application using real data.

The heavy rainfall event that occurred on 5–6 July 2017 in Northern Kyushu, Japan, caused extensive flooding across several mountainous river basins and resulted in fatalities and extensive damage to infrastructure along those rivers. For the periods before and during the extreme event, there are no hydrological observations for many of the flooded river basins, most of which are small and located in mountainous regions. We used the Gridded Surface Subsurface Hydrologic Analysis (GSSHA) model, a physically based model, to acquire more detailed information about the hydrological processes in the flood-affected ungauged mountain basins. We calibrated the GSSHA model using data from an adjacent gauged river basin, and then applied it to several small ungauged basins without changing the parameters of the model. We simulated the gridded flow and generated a map of the possible maximum flood depth across the basins. By comparing the extent of flood-affected areas from the model with data of the Japanese Geospatial Information Authority (GSI), we found that the maximum flood inundation areas of the river networks estimated by the GSSHA model are sometimes less than those estimated by the GSI, as the influence of landslides and erosion was not considered in the modeling. The model accuracy could be improved by taking these factors into account, although this task would be challenging. The results indicated that simulations of flood inundation in ungauged mountain river basins could contribute to disaster management during extreme rain events.

High accuracy retrieval algorithm is developed for integrated water vapor content (WVC) retrieval from Advanced Microwave Sounding Radiometer 2 (AMSR2) measurements over open ocean areas. The algorithm is based on physical modeling of the brightness temperature (BT) of the upwelling radiation of the atmosphere — ocean system. The brightness temperature inversion is carried out with Neural Networks (NNs), trained on an ensemble of BTs, calculated using the data set of the atmospheric and oceanic parameters, governing passive microwave radiation of the atmosphere — ocean system. The improvement in the WVC retrieval is associated with the usage of the new ocean emissivity empirical model and exclusion of vertically polarized BT from the NNs inputs. The new model was incorporated into BT geophysical model and a new set of NNs coefficients was obtained for WVC algorithm. Though the results of the numerical experiment demonstrate higher retrieval accuracy for the old version of the NN model, real-valued validation with Global Positioning System WVC shows better performance of the new NN model with excluded vertically polarized measurements from NN inputs. The advantages of the new algorithm are the most remarkable under conditions of high winds. This is especially important in the studies of extreme weather events such as Polar Lows, Extratropical and Tropical Cyclones associated with high winds. Examples of WVC retrievals under extreme events are given.

Climate change is proceeding at an unprecedented pace with global temperatures and sea-levels setting new records almost every year (IPCC, 2007). While these changes are worrisome due to effects on all biological systems and hence also on humans, even more problematic changes may be in the waiting, because not only is the climate changing, but it is also becoming more extreme. Extreme temperatures, rainfall, droughts, storms and fires are already becoming more common with severe consequences for humans, their crops and domestic animals and all wild organisms. For example, the severe heat wave in 2003 caused an excess mortality of 2,600 humans in France alone (INSERM, 2003), and primary production was suppressed across Europe (Ciais et al. 2004). There is a long history of biological studies of extreme events going back to Bumpus’ (1895) study of mortality and selection on house sparrows Passer domesticus during a severe snowstorm. Extreme climatic events are poorly studied simply because they are rare, and such events have been defined to happen less than 5% of the time relative to the expected distribution (http://www.emc.ncep.noaa.gov). This lack of studies of the biological consequences is highly problematic because we know very little about the ability of plants and animals to adapt to such extreme situations. Here a number of specialists reviewed the scattered literature on effects of extreme climate change. Moller starts by analyzing the behavioral effects of extreme climatic events, while Wingfield et al. review the physiological underpinnings of such behavioral responses. Next, Moreno & Moller review the demographic and life-history consequences of extreme climatic conditions, showing that fecundity and survival are dramatically reduced. Dolenec et al. analyze a case study of response of a bird species to extreme climatic conditions. Martinez & Merino provide an over-view of the parasitological consequences of extreme climate and review the consequences for domestic animals and humans. Finally, Jiguet et al. provide a review of the consequences of extreme climatic events on communities of animals. This special section on biological effects of extreme climate change raises many questions and provides guidelines for future studies in this area of major significance.

Strengthening the combination of science and technology finance is an important means to implement innovation driven development strategy.Since 2011, the Ministry of science and technology in conjunction with the eight ministries, the Ministry of finance, people's Bank of China and other selected 16 Beijing Zhongguancun, Chengdu hi tech Zone, Shanghai, Wuhan and other areas, to actively promote the combination of technology and finance pilot work, explore the new mechanism of scientific and technological resources and financial resources docking, and made significant progress.This paper attempts to sum up the experience of the pilot areas of scientific and technological financial innovation, in order to provide a good reference for the further development of Inner Mongolia's science and technology finance.

There has been a paucity of information on trends in hydrological extremes. Based on daily precipitation and temperature and streamflow records in the arid region, northwest of China, the temporal and spatial characteristics of hydrological extremes were analyzed during 1960–2010. The results showed that: (1) The temperature extremes show patterns consistent with warming, with a large proportion of stations showing statistically significant trends. Warming trends in indices derived from daily minimum temperature are of greater magnitudes than those from maximum temperature. The decreases in frequency for cold extremes mainly occur in summer and autumn, while warm extremes show significant increases in frequency in autumn and winter; (2) Most precipitation indices exhibited increasing trends across the region, and the precipitation increase in the arid region was due to the increase in both precipitation frequency and intensity; (3) There were increasing trends for frequency of extreme hydrological events from 1901 to 2010, particularly post 1970s. Extreme hydrological events occurred mainly during summer. Based on the results obtained in this study, the frequency, magnitude, and intensity of extreme hydrological events are expected to increase over time; (4) Frequency distribution exhibited a general symmetry along the Tianshan Mountains, distributed evenly in Junggar Basin and Tarim Basin. More extremes were observed in the north-west than that in the southeast. The maximum incidence was in west Tianshan Mountains and generally decreased south-eastward.

Reviewing recent literature, we report that changes in extreme heat event characteristics such as magnitude, frequency, and duration are highly sensitive to changes in mean global-scale warming. Numerous studies have detected significant changes in the observed occurrence of extreme heat events, irrespective of how such events are defined. Further, a number of these studies have attributed present-day changes in the risk of individual heat events and the documented global-scale increase in such events to anthropogenic-driven warming. Advances in process-based studies of heat events have focused on the proximate land-atmosphere interactions through soil moisture anomalies, and changes in occurrence of the underlying atmospheric circulation associated with heat events in the midlatitudes. While evidence for a number of hypotheses remains limited, climate change nevertheless points to tail risks of possible changes in heat extremes that could exceed estimates generated from model outputs of mean temperature. We also explore risks associated with compound extreme events and nonlinear impacts associated with extreme heat.

A counterfactual perspective on compound weather risk

This paper presents a data-driven approach for quantifying the resilience of distribution power grids to extreme weather events using two key metrics: (a) the number of outages and (b) restoration time. The method leverages historical outage records maintained by power utilities and weather measurements collected by the National Oceanic and Atmospheric Administration (NOAA) to evaluate resilience across a utility’s service territory. The proposed framework consists of three stages. First, outage events are systematically extracted from the outage records by temporally and spatially aggregating coincident component outages. In the second stage, weather zones across the service territory are delineated using a Voronoi polygon approach, based on the locations of NOAA weather sensors. Finally, data-driven models for outage fragility and restoration time are developed for each weather zone. These models enable the quantification and visualization of resilience metrics under varying intensities of extreme weather events. The proposed method is demonstrated using real-world data from a Midwestern US distribution utility, focused on wind- and precipitation-related events. The dataset spans two decades and includes over 160,000 outage records. The data-driven models accurately capture the nonlinear relationship between weather intensity, outage accumulation, and restoration time, and the resulting zone-specific resilience maps provide utilities with actionable insights for prioritizing hardening and operational planning.