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 Estimating Reliability of a Stress – Strength Model in Case of Rayleigh Pareto Distribution

The stress – strength model is one of the models that are used to compute reliability. In this paper, we derived mathematical formulas for the reliability of the stress – strength model that follows Rayleigh Pareto (Rayl. – Par) distribution. Here, the model has a single component, where strength Y is subjected to a stress X, represented by moment, reliability function, restricted behavior, and ordering statistics. Some estimation methods were used, which are the maximum likelihood, ordinary least squares, and two shrinkage methods, in addition to a newly suggested method for weighting the contraction. The performance of these estimates was studied empirically by using simulation experimentation that could give more varieties for different-sized samples for stress and strength. The most interesting finding indicates the superiority of the proposed shrinkage estimation method.

Analysis of Transmission of Hepatitis C Viruses: Dental vs. Surgical Procedures

Objectives: The primary purpose of the present study is to evaluate the cause of HCV transmission either by dental or surgical procedures in Pakistan. It will reveal the standards of current practices and knowledge of surgical instrument sterilization in Pakistan. Methods:The contemporary study design was cross-sectional. A total of 7097 patients were included in the study that was the confirmed cases of Hepatitis C from four districts of Punjab, Pakistan, during the period of three years from Jul 1, 2018, to Jun 30, 2021. The ANN model simulates a discrete Pareto distribution; descriptive statistics were applied by using SPSS 23.Results:In age distribution, most patients were aged 26-37 from the 2020- 2021 year of study with 45.6%age. The total mean ± SD was 2.42 ± .935 with 0.000P-values. Results show that high-risk variables are strongly associated with the surgical history, such as sector analysis (public and private) with 0.000 P-values. Analysis of these variables indicated that inquiry about surgical instruments sterilization and age groups(100%)were the most vital variable in the ANN model. Pareto distribution values of surgical procedures that are transmitting hepatitis C viruses more than the dental procedures. Conclusion: Surgical procedures are high transmission source of hepatitis C viruses than dental procedures. Clinical Significance: More care should be taken, and more severe sterilization measures should be taken to prevent the transmission of hepatitis C infection, especially in dental and general surgery procedures in Pakistan.

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.

Generalized Confidence Intervals for Zero-Inflated Pareto Distribution

This paper considers interval estimations for the mean of Pareto distribution with excess zeros. Three approaches for interval estimation are proposed based on fiducial generalized pivotal quantities (FGPQs), respectively. Simulation studies are performed to assess the performance of the proposed methods, along with three measurements to determine comparisons with competing approaches. The advantages and disadvantages of each method are provided. The methods are illustrated using a real phone call dataset.