Bayesian and non-Bayesian estimation of the Lomax model based on upper record values under weighted LINEX loss function

In this article, we developed a new loss function, as the simplification of linear exponential loss function (LINEX) by weighting LINEX function. We derive a scale parameter, reliability and the hazard functions in accordance with upper record values of the Lomax distribution (LD). To study a small sample behavior performance of the proposed loss function using a Monte Carlo simulation, we make a comparison among maximum likelihood estimator, Bayesian estimator by means of LINEX loss function and Bayesian estimator using square error loss (SE) function. The consequences have shown that a modified method is the finest for valuing a scale parameter, reliability and hazard functions

Bayes Estimation of Pareto Distribution Based on Type II Censored Data under the Weighted LINEX Loss Function

The main objective of this article is to develop a linear exponential function risks in Saudi banks (LINEXLF) to estimate the shape parameter, reliability, and hazard rate functions of the Pareto distribution based on Type II Censored Data. By weighting LINEX loss function to produce a modified loss function called weighted linear exponential (WLINEXLF) loss function. We then use WLINEXLF to derive the shape parameter, reliability, and hazard rate functions of the Pareto distribution. Furthermore, to examine the performance of the proposed method WLINEXLF we conduct a Monte Carlo simulation. The comparison is between the proposed method and other methods including maximum likelihood estimation (MLE) and Bayesian estimation under the squared error loss function. The results of the simulation show that the proposed method WLINEXLF in this article has the best performance in estimating shape parameter, reliability, and hazard rate functions, according to the smallest values of mean squared error (MSE). This result means that the proposed method can be applied in real data in banking industrial sectors. This paper aims to use the modified loss function to estimate the shape parameter, reliability (), and hazard rate functions h() in Saudi banks of the Pareto distribution based on Type II Censored Data

Bayesian Estimations under the Weighted LINEX Loss Function Based on Upper Record Values

The essential objective of this research is to develop a linear exponential (LINEX) loss function to estimate the parameters and reliability function of the Weibull distribution (WD) based on upper record values when both shape and scale parameters are unknown. We perform this by merging a weight into LINEX to produce a new loss function called the weighted linear exponential (WLINEX) loss function. Then, we utilized WLINEX to derive the parameters and reliability function of the WD. Next, we compared the performance of the proposed method (WLINEX) in this work with Bayesian estimation using the LINEX loss function, Bayesian estimation using the squared-error (SEL) loss function, and maximum likelihood estimation (MLE). The evaluation depended on the difference between the estimated parameters and the parameters of completed data. The results revealed that the proposed method is the best for estimating parameters and has good performance for estimating reliability

Bayesian Analysis of Record Statistic from the Inverse Weibull Distribution under Balanced Loss Function

The main contribution of this work is to develop a linear exponential loss function (LINEX) to estimate the scale parameter and reliability function of the inverse Weibull distribution (IWD) based on lower record values. We do this by merging a weight into LINEX to produce a new loss function called weighted linear exponential loss function (WLINEX). We then use WLINEX to derive the scale parameter and reliability function of the IWD. Subsequently, we discuss the balanced loss functions for three different types of loss function, which include squared error (SE), LINEX, and WLINEX. The majority of previous scholars determined the weighted balanced coefficients without mathematical justification. One of the main contributions of this work is to utilize nonlinear programming to obtain the optimal values of the weighted coefficients for balanced squared error (BSE), balanced linear exponential (BLINEX), and balanced weighted linear exponential (BWLINEX) loss functions. Furthermore, to examine the performance of the proposed methods—WLINEX and BWLINEX—we conduct a Monte Carlo simulation. The comparison is between the proposed methods and other methods including maximum likelihood estimation, SE loss function, LINEX, BSE, and BLINEX. The results of simulation show that the proposed models BWLINEX and WLINEX in this work have the best performance in estimating scale parameter and reliability, respectively, according to the smallest values of mean SE. This result means that the proposed approach is promising and can be applied in a real environment

Nonlinear Programming to Determine Best Weighted Coefficient of Balanced LINEX Loss Function Based on Lower Record Values

Majority research studies in the literature determine the weighted coefficients of balanced loss function by suggesting some arbitrary values and then conducting comparison study to choose the best. However, this methodology is not efficient because there is no guarantee ensures that one of the chosen values is the best. This encouraged us to look for mathematical method that gives and guarantees the best values of the weighted coefficients. The proposed methodology in this research is to employ the nonlinear programming in determining the weighted coefficients of balanced loss function instead of the unguaranteed old methods. In this research, we consider two balanced loss functions including balanced square error (BSE) loss function and balanced linear exponential (BLINEX) loss function to estimate the parameter and reliability function of inverse Rayleigh distribution (IRD) based on lower record values. Comparisons are made between Bayesian estimators (SE, BSE, LINEX, and BLINEX) and maximum likelihood estimator via Monte Carlo simulation. The evaluation was done based on absolute bias and mean square errors. The outputs of the simulation showed that the balanced linear exponential (BLINEX) loss function has the best performance. Moreover, the simulation verified that the balanced loss functions are always better than corresponding loss function

A unique Markov chain Monte Carlo method for forecasting wind power utilizing time series model

Concerns that impair human societies frequently include a heavy dependence on petroleum and coal and emissions of greenhouse gases. Thus, adopting renewable energy sources, such as wind power, has become a practical solution to this problem. Therefore, to carry out the research on wind velocity energy, a time-series structure is necessary. This study uses the Markov chain Monte Carlo approach and the Seasonal Autoregressive Integrated Moving Average (SARIMA) model to estimate short-term and long-term sustained winds. The significance of building a wind energy system is initially discussed, after which a wind velocity time-series framework based on a SARIMA is presented, followed by a short-term and Long-term wind speed projection. Furthermore, a methodology utilizing the Markov chain Monte Carlo method (MCMC) is suggested to establish a wind energy time-series analysis. This framework draws a Markov chain for time-series data on wind energy to maintain stochasticity and realize the probability transition matrix. Gibbs sampling is employed as well. The model's forecasting abilities were tested using the original database and various efficiency assessment measures, including Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE) with efficiency of 13.09 and 1.03. In this study, a framework with the highest KGE and WI as well as the lowest RMSE and MAE was chosen. The findings demonstrate that the approach used in the operation provides outstanding predictability

A Theoretical and Numerical Study on Fractional Order Biological Models with Caputo Fabrizio Derivative

This article studies a biological population model in the context of a fractional Caputo-Fabrizio operator using double Laplace transform combined with the Adomian method. The conditions for the existence and uniqueness of solution of the problem under consideration is established with the use of the Banach principle and some theorems from fixed point theory. Furthermore, the convergence analysis is presented. For the accuracy and validation of the technique, some applications are presented. The numerical simulations present the obtained approximate solutions with a variety of fractional orders. From the numerical simulations, it is observed that when the fractional order is large, then the population density is also large; on the other hand, population density decreases with the decrease in the fractional order. The obtained results reveal that the considered technique is suitable and highly accurate in terms of the cost of computing, and can be used to analyze a wide range of complex non-linear fractional differential equations

A Theoretical and Numerical Study on Fractional Order Biological Models with Caputo Fabrizio Derivative

This article studies a biological population model in the context of a fractional Caputo-Fabrizio operator using double Laplace transform combined with the Adomian method. The conditions for the existence and uniqueness of solution of the problem under consideration is established with the use of the Banach principle and some theorems from fixed point theory. Furthermore, the convergence analysis is presented. For the accuracy and validation of the technique, some applications are presented. The numerical simulations present the obtained approximate solutions with a variety of fractional orders. From the numerical simulations, it is observed that when the fractional order is large, then the population density is also large; on the other hand, population density decreases with the decrease in the fractional order. The obtained results reveal that the considered technique is suitable and highly accurate in terms of the cost of computing, and can be used to analyze a wide range of complex non-linear fractional differential equations

A generalized framework for quantifying and monitoring the severity of meteorological drought

The current study proposes a new framework for quantifying and monitoring the severity of meteorological drought. The proposed framework consists of three phases. The first phase of the framework uses K-component Gaussian Mixture Distribution (GMD) in the computation. The second phase is mainly based on the dissimilarity matrix-based clustering using C-index and Monte Carlo Feature-based Selection (MCFS) method. The third phase uses the Markov chain, transition probabilities and a non-homogeneous Poisson process under the Bayesian estimation. The Relative Importance (RI) values are used to choose appropriate stations. The Deviance Information Criteria (DIC) is used to check model suitability, and Root Mean Square Error (RMSE) is utilized for determining model performance. The proposed framework is validated to the 52 meteorological stations in Pakistan for 49 years from 1968 to 2016. Moreover, the outcomes of the current analysis provide insight to quantify and monitor meteorological drought comprehensively and accurately

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