Modeling Extreme Values Utilizing an Asymmetric Probability Function

In this article, a new flexible probability density function with three parameters is proposed for modeling asymmetric data (positive and negative) with different types of kurtosis (mesokurtic, leptokurtic and platykurtic). Some of its statistical and reliability properties, including hazard rate function, moments, moment generating function, incomplete moments, mean deviations, moment of the residual life, moment of the reversed residual life, and order statistics are derived. Its hazard rate function can be either constant, increasing-constant, decreasing-constant, U shape, upside down shape or upside down-U shape. Seven classical estimation methods are considered to estimate the unknown model parameters. Monte Carlo simulation experiments are performed to compare the performance of the seven different estimation methods. Finally, a distinctive asymmetric real data application is analyzed for illustrating the flexibility of the new model

Classical and Fixed Point Approach to the Stability Analysis of a Bilateral Symmetric Additive Functional Equation in Fuzzy and Random Normed Spaces

In this article, a new kind of bilateral symmetric additive type functional equation is introduced. One of the interesting characteristics of the equation is the fact that it is ideal for investigating the Ulam–Hyers stabilities in two prominent normed spaces, namely fuzzy and random normed spaces simultaneously. This article analyzes the proposed equation in both spaces. The solution of this equation exhibits the property of symmetry, that is, the left of the object becomes the right of the image, and vice versa. Additionally, the stability results of this functional equation are determined in fuzzy and random normed spaces using direct and fixed point methods

Classical and Fixed Point Approach to the Stability Analysis of a Bilateral Symmetric Additive Functional Equation in Fuzzy and Random Normed Spaces

In this article, a new kind of bilateral symmetric additive type functional equation is introduced. One of the interesting characteristics of the equation is the fact that it is ideal for investigating the Ulam–Hyers stabilities in two prominent normed spaces, namely fuzzy and random normed spaces simultaneously. This article analyzes the proposed equation in both spaces. The solution of this equation exhibits the property of symmetry, that is, the left of the object becomes the right of the image, and vice versa. Additionally, the stability results of this functional equation are determined in fuzzy and random normed spaces using direct and fixed point methods

Stability Analysis of a New Class of Series Type Additive Functional Equation in Banach Spaces: Direct and Fixed Point Techniques

In this paper, the authors introduce two new classes of series type additive functional Equations (FEs). The first class of equations is derived from the sum of the squares of the alternative series and the second one is obtained from the sum of the cubes of the series. The solution of the FE is investigated using the principle of mathematical induction. The beauty of this method lies in the fact that it satisfies the property of the additive FE as well as the series. Banach spaces are one of the widely-used spaces that are very helpful to analyse the stability results of various FEs. The Banach space conditions have been applied and the stability results are established for both of the equations. Furthermore, the Banach Contraction principle and alternative of fixed point theorem are used to derive the stability results in a fixed point technique (FPT). The relationship between the FEs and both the series is established through the principle of mathematical induction in the Application section, which adds novelty to the derived results

Optimization of meteorological monitoring network of New South Wales, Australia

Several climatic variables like precipitation, temperature, fog, dew, humidity, and wind significantly impact agricultural production. While formulating policies for agriculture and other industrial sectors, precise knowledge regarding climatic variables is essential and helpful. The Bureau of Meteorology (BOM) monitored various climatic variables at more than 226 meteorological stations in New South Wales (NSW), Australia. However, the placement of these monitoring stations was not systematic. As a result, predictions for unobserved sites turn out to be erroneous. Inadequate or poorly placed meteorological stations can lead to inaccurate weather forecasts, make it difficult to fully understand local and regional weather patterns, and, lastly, make it impossible to identify the early warnings for severe weather events like hurricanes, tornadoes, and flash floods. Therefore, the study aims to optimize and suggest a monitoring network to minimize the prediction error of these climatic variables. The optimized monitoring network can be found by optimally adding new meteorological monitoring stations or withdrawing existing ones while still ensuring the reliability of weather data. In this study, the meteorological monitoring network of NSW, Australia was optimized using two stochastic search algorithms: Spatial Simulated Annealing (SSA) and Genetic Algorithms (GA). The Average Kriging Variance (AKV) is considered an accuracy measure for SSA and GA. Ordinary kriging (OK) and Universal Kriging (UK), two popular prediction methods, are used using covariation modeled by the Matheron variogram model. The results reveal that the time consumption for SSA and GA are relatively similar, but the SSA utilizing the UK gives a lower AKV than GA. The optimized meteorological monitoring will be useful for ensuring accurate weather forecasts, providing early warnings of severe weather events, and enabling scientific research to understand and mitigate the effects of climate change. Furthermore, this novel optimization strategy will not only be helpful for the government of Australia but will significantly improve prediction accuracy, providing more reliable information for various weather-related activities, such as agriculture, construction, and emergency management

A new comprehensive approach for regional drought monitoring

The Standardized Precipitation Index (SPI) is a vital component of meteorological drought. Several researchers have been using SPI in their studies to develop new methodologies for drought assessment, monitoring, and forecasting. However, it is challenging for SPI to provide quick and comprehensive information about precipitation deficits and drought probability in a homogenous environment. This study proposes a Regional Intensive Continuous Drought Probability Monitoring System (RICDPMS) for obtaining quick and comprehensive information regarding the drought probability and the temporal evolution of the droughts at the regional level. The RICDPMS is based on Monte Carlo Feature Selection (MCFS), steady-state probabilities, and copulas functions. The MCFS is used for selecting more important stations for the analysis. The main purpose of employing MCFS in certain stations is to minimize the time and resources. The use of MCSF makes RICDPMS efficient for drought monitoring in the selected region. Further, the steady-state probabilities are used to calculate regional precipitation thresholds for selected drought intensities, and bivariate copulas are used for modeling complicated dependence structures as persisting between precipitation at varying time intervals. The RICDPMS is validated on the data collected from six meteorological locations (stations) of the northern area of Pakistan. It is observed that the RICDPMS can monitor the regional drought and provide a better quantitative way to analyze deficits with varying drought intensities in the region. Further, the RICDPMS may be used for drought monitoring and mitigation policies

Effect of Fuzzy Time Series on Smoothing Estimation of the INAR(1) Process

In this paper, the effect of fuzzy time series on estimates of the spectral, bispectral and normalized bispectral density functions are studied. This study is conducted for one of the integer autoregressive of order one (INAR(1)) models. The model of interest here is the dependent counting geometric INAR(1) which is symbolized by (DCGINAR(1)). A realization is generated for this model of size n = 500 for estimation. Based on fuzzy time series, the forecasted observations of this model are obtained. The estimators of spectral, bispectral and normalized bispectral density functions are smoothed by different one- and two-dimensional lag windows. Finally, after the smoothing, all estimators are studied in the case of generated and forecasted observations of the DCGINAR(1) model. We investigate the contribution of the fuzzy time series to the smoothing of these estimates through the results

A New Bayesian Network-Based Generalized Weighting Scheme for the Amalgamation of Multiple Drought Indices

Drought is one of the most multifaceted hydrologic phenomena, affecting several factors such as soil moisture, surface runoff, and significant water shortages. Therefore, monitoring and assessing drought occurrences based on a single drought index are inadequate. The current study develops a multiscalar weighted amalgamated drought index (MWADI) to amalgamate multiple drought indices. The MWADI is mainly based on the normalized average dependence posterior probabilities (ADPPs). These ADPPs are obtained from Bayesian networks (BNs)-based Markov Chain Monte Carlo (MCMC) simulations. Results have shown that the MWADI correlates more with the standardized precipitation index (SPI) and the standardized precipitation temperature index (SPTI). As proposed, the MWADI synthesizes drought characteristics of different multiscalar drought indices to reduce the uncertainty of individual drought indices and provide a comprehensive drought assessment.Validerad;2023;Nivå 2;2023-05-04 (hanlid);Funder: Deanship ofScientifc Research at King Khalid University  (RGP.2/23/44); Prince Sattam bin Abdulaziz University (PSAU/2023/R/1444);Part of special issue: Technologies-Based Advanced Machine Learning Models: Applications in Civil Engineering 2021</p

Effect of Fuzzy Time Series on Smoothing Estimation of the INAR(1) Process

In this paper, the effect of fuzzy time series on estimates of the spectral, bispectral and normalized bispectral density functions are studied. This study is conducted for one of the integer autoregressive of order one (INAR(1)) models. The model of interest here is the dependent counting geometric INAR(1) which is symbolized by (DCGINAR(1)). A realization is generated for this model of size n = 500 for estimation. Based on fuzzy time series, the forecasted observations of this model are obtained. The estimators of spectral, bispectral and normalized bispectral density functions are smoothed by different one- and two-dimensional lag windows. Finally, after the smoothing, all estimators are studied in the case of generated and forecasted observations of the DCGINAR(1) model. We investigate the contribution of the fuzzy time series to the smoothing of these estimates through the results

Proposing a new framework for analyzing the severity of meteorological drought

The quantitative description of meteorological drought from various geographical locations and indicators is crucial for early drought warning to avoid its negative impacts. Therefore, the current study proposes a new framework to comprehensively accumulate spatial and temporal information for meteorological drought from various stations and drought indicators (indices). The proposed framework is based on two major components such as the Monthly-based Monte Carlo Feature Selection (MMCFS,) and Monthly-based Joint Index Weights (MJIW). Besides, three commonly used SDI are jointly assessed to quantify drought for selected geographical locations. Moreover, the current study uses the monthly data from six meteorological stations in the northern region for 47 years (1971-2017) for calculating SDI values. The outcomes of the current research explicitly accumulate regional spatiotemporal information for meteorological drought. In addition, results may serve as an early warning to the effective management of water resources to avoid negative drought impacts in Pakistan