Search Results (358)

The generalized Pareto distribution is frequently used for modeling extreme values above an appropriate threshold level. Since the process of determining the appropriate threshold value is difficult, a mixture of extreme value models rises to prominence. In this study, mixture extreme value models based on exponentiated Pareto distribution are proposed. The Weibull, gamma, and log-normal models are used as bulk densities. The parameter estimates of the proposed models are obtained using the maximum likelihood approach. Two different approaches based on maximization of the log-likelihood and Kolmogorov–Smirnov p-value are used to determine the appropriate threshold value. The effectiveness of these methods is compared using simulation studies. The proposed models are compared with other mixture models through an application study on earthquake data. The GammaEP web application is developed to ensure the reproducibility of the results and the usability of the proposed model. Full article

Groundwater is essential for irrigated agriculture, yet its use remains unsustainable in many regions worldwide. In countries like Pakistan, the situation is particularly pressing. The irrigated agriculture of Pakistan heavily relies on groundwater resources owing to limited canal-water availability. The groundwater quality in the region ranges from good to poor, with the lower-quality water adversely affecting soil structure and plant health, leading to reduced agricultural productivity. The delineation of quality zones with respect to irrigation parameters is thus crucial for optimizing its sustainable use and management. Therefore, this research study was carried out in the Lower Chenab Canal (LCC) irrigation system to assess the spatial distribution of groundwater quality. The geostatistical analysis was conducted using Gamma Design Software (GS+) and the Kriging interpolation method was applied within a Geographic Information System (GIS) framework to generate groundwater-quality maps. Semivariogram models were evaluated for major irrigation parameters such as electrical conductivity (EC), residual sodium carbonate (RSC), and sodium adsorption ratio (SAR) to identify the best fit for various Ordinary Kriging models. The spherical semivariogram model was the best fit for EC, while the exponential model best suited SAR and RSC. Overlay analysis was performed to produce combined water-quality maps. During the pre-monsoon season, 17.83% of the LCC area demonstrated good irrigation quality, while 42.84% showed marginal quality, and 39.33% was deemed unsuitable for irrigation. In the post-monsoon season, 17.30% of the area had good irrigation quality, 44.53% exhibited marginal quality, and 38.17% was unsuitable for irrigation. The study revealed that Electrical Conductivity (EC) was the primary factor affecting water quality, contributing to 71% of marginal and unsuitable conditions. In comparison, the Sodium Adsorption Ratio (SAR) accounted for 38% and Residual Sodium Carbonate (RSC) contributed 45%. Therefore, it is recommended that groundwater in unsuitable zones be subjected to artificial recharge methods and salt-tolerated crops to enhance its suitability for agricultural applications. Full article

This paper explores statistical techniques for estimating unknown lifetime parameters using data from a progressive first-failure censoring scheme. The failure times are modeled with a new Weibull–Pareto distribution. Maximum likelihood estimators are derived for the model parameters, as well as for the survival and hazard rate functions, although these estimators do not have explicit closed-form solutions. The Newton–Raphson algorithm is employed for the numerical computation of these estimates. Confidence intervals for the parameters are approximated based on the asymptotic normality of the maximum likelihood estimators. The Fisher information matrix is calculated using the missing information principle, and the delta technique is applied to approximate confidence intervals for the survival and hazard rate functions. Bayesian estimators are developed under squared error, linear exponential, and general entropy loss functions, assuming independent gamma priors. Markov chain Monte Carlo sampling is used to obtain Bayesian point estimates and the highest posterior density credible intervals for the parameters and reliability measures. Finally, the proposed methods are demonstrated through the analysis of a real dataset. Full article

The paper presents an enhanced numerical framework for computing the one-dimensional fast Fractional Fourier Transform (FRFT) by integrating closed-form Composite Newton-Cotes quadrature rules. We show that a FRFT of a $QN$-length weighted sequence can be decomposed analytically into two mathematically commutative compositions: one involving the composition of a FRFT of an N-length sequence and a FRFT of a Q-length weighted sequence, and the other in reverse order. The composite FRFT approach is applied to the inversion of Fourier and Laplace transforms, with a focus on estimating probability densities for distributions with complex-valued characteristic functions. Numerical experiments on the Variance-Gamma (VG) and Generalized Tempered Stable (GTS) models show that the proposed scheme significantly improves accuracy over standard (non-weighted) fast FRFT and classical Newton-Cotes quadrature, while preserving computational efficiency. The findings suggest that the composite FRFT framework offers a robust and mathematically sound tool for transform-based numerical approximations, particularly in applications involving oscillatory integrals and complex-valued characteristic functions. Full article

The thermal Doppler broadening of spectral profiles for particle populations in the absence or presence of potential fields can be described by kappa distributions. The kappa distribution provides a replacement for the Maxwell–Boltzmann distribution, which can be considered as a generalization for describing systems characterized by local correlations among their particles, as found in space and astrophysical plasmas. This paper presents all special cases of kappa distributions as members of a general pathway family of densities introduced by Mathai. The aim of the present paper is to bring to attention the application of various forms of the kappa distribution, its various special cases and its generalizations, which, in scalar-variable and multivariate situations, belong to a general family of distributions known as Mathai’s pathway models, comprising three different families of functions, namely the generalized type-1 beta, type-2 beta and gamma families. Through one parameter, known as the pathway parameter, one will be able to reach all the three families of functions and the stages of transitioning from one family to another. After pointing out the connection of multivariate (vector-variate) kappa distributions to the multivariate pathway model, the multivariate kappa distribution is extended to the real matrix-variate case by working out the various forms and by evaluating the normalizing constants of the various forms of the matrix-variate case explicitly. It is also pointed out that the pathway models are available for the scalar, vector and rectangular matrix-variate cases in the real domain as well as in the complex domain. Full article

The point-kernel (PK) technique has a long history in applied radiation shielding, originating from the early days of digital computers. The PK technique applied to gamma-ray attenuation is one of many successful applications, based on the linear superposition principle applied to distributed radiation sources. Mathematically speaking, the distributed source will produce a detector response equivalent to the numerical integration of the radiation received from an equivalent number of point sources. In this treatment, there is no interference between individual point sources, while inherent limitations of the PK method are its inability to simulate gamma scattering in shields and the usage of simple boundary conditions. The PK method generally works for gamma-ray shielding with corrective B-factor for scattering and only specifically for fast neutron attenuation in a hydrogenous medium with the definition of cross section removal. This paper presents theoretical and programming aspects of the PK program developed for a distributed source of photons (line, disc, plane, sphere, slab volume, etc.) and slab shields. The derived flux solutions go beyond classical textbooks as they include the analytical integration of Taylor B-factor, obtaining a closed form readily suitable for programming. The specific computational modules are unified with a graphical user interface (GUI), assisting users with input/output data and visualization, developed for the fast radiological characterization of simple shielding problems. Numerical results of the selected PK test cases are presented and verified with the CADIS hybrid shielding methodology of the MAVRIC/SCALE6.1.3 code package from the ORNL. Full article

This study was realized in the frame of an IAEA Coordinated Research Project for the evaluation of sediment dynamics, applying in-situ radiometric methods accompanied with a theoretical model. The in-situ methods were validated using lab-based high-resolution gamma-ray spectrometry. Sediment dynamics assessments were performed based on the measured and mapped activity concentrations of specific ²³⁸U progenies (²¹⁴Bi or ²¹⁴Pb), ²³²Th progenies (²⁰⁸Tl and ²²⁸Ac), and ⁴⁰K along the shoreline of the beach. The maps of the activity concentrations of natural radionuclides were produced rapidly using software tools (R language v4.5). The sediment dynamics of the studied area were also investigated through numerical simulations, applying an open source model considering land–sea interactions and meteorological conditions and the corresponding sediment processes. The assessments, which were conducted utilizing the detailed data from the natural radioactivity maps, were validated by the simulation results, since both were found to be in agreement. Generally, it was confirmed that the distribution of radionuclides reflects the selective transport processes of sediments, which are related to the corresponding processes that occur in the study area. Legrena Beach in Attica, Greece, served as a pilot area for the comparative analysis of methods and demonstration of their relevance and applicability for studying coastal processes. Full article

The instability of the geopolitical situation due to the high terrorist danger leads to the need to take into account at the planning stage the capabilities of intruders to perform UAV flight missions. A general method for analyzing the process of cargo delivery by UAVs (Unmanned Aerial Vehicles) to hard-to-reach areas during emergencies has been proposed. This method allows for the evaluation of UAV effectiveness based on the probability of successful cargo delivery within a specified time limit. The method is based on applying topological transformation techniques to stochastic networks. The cargo delivery process is modeled as a stochastic network, followed by the determination of its equivalent function and the use of Heaviside decomposition to calculate the distribution function and the expected delivery time. This presentation of the studied process for the first time made it possible to take into account the impact on the flight mission of the UAV of the destructive impact from the attacker. This approach allows the destructive effects on the UAV from malicious interference to be considered. The input data used for the analysis are parameters that characterize the properties of individual processes within the stochastic network, represented as branches, which are computed using methodologies published in earlier studies. It has been demonstrated that the resulting distribution function of the mission completion time can be accurately approximated by a gamma distribution with a level of precision suitable for practical applications. In this case, the gamma distribution parameters are determined using the equivalent function of the stochastic network. The proposed method can be used by flight planners when scheduling UAV operations in emergency zones, especially in scenarios where there is a risk of malicious interference. Full article

This article presents maximum likelihood and Bayesian estimates for the parameters, reliability function, and hazard function of the Gumbel Type-II distribution using a unified hybrid censored sample. Bayesian estimates are derived under three loss functions: squared error, LINEX, and generalized entropy. The parameters are assumed to follow independent gamma prior distributions. Since closed-form solutions are not available, the MCMC approximation method is used to obtain the Bayesian estimates. The highest posterior density credible intervals for the model parameters are computed using importance sampling. Additionally, approximate confidence intervals are constructed based on the normal approximation to the maximum likelihood estimates. To derive asymptotic confidence intervals for the reliability and hazard functions, their variances are estimated using the delta method. A numerical study compares the proposed estimators in terms of their average values and mean squared error using Monte Carlo simulations. Finally, a real dataset is analyzed to illustrate the proposed estimation methods. Full article

The research focuses on probabilistic modeling of maximum rainfall in Zielona Góra, Poland, to improve urban drainage system design. The study utilizes archived pluviographic data from 1951 to 2020, collected at the IMWM-NRI meteorological station. These data include 10 min rainfall records and aggregated hourly and daily totals. The study employs various statistical distributions, including Fréchet, gamma, generalized exponential (GED), Gumbel, log-normal, and Weibull, to model rainfall intensity–duration–frequency (IDF) relationships. After testing the goodness of fit using the Anderson–Darling test, Bayesian Information Criterion (BIC), and relative residual mean square Error (rRMSE), the GED distribution was found to best describe rainfall patterns. A key outcome is the development of a new rainfall model based on the GED distribution, allowing for the estimation of precipitation amounts for different durations and exceedance probabilities. However, the study highlights limitations, such as the need for more accurate local models and a standardized rainfall atlas for Poland. Full article

This study investigates the performance of a mixed dual-hop free-space optical/underwater wireless optical communication (FSO-UWOC) system employing a decode-and-forward (DF) relay protocol, particularly under a comprehensive hybrid channel fading model. The FSO link is assumed to experience Gamma–Gamma atmospheric turbulence fading, combined with air path loss and pointing errors. Meanwhile, the UWOC link is modeled with generalized Gamma distribution (GGD) oceanic turbulence fading, along with underwater path loss and pointing errors. Based on the proposed hybrid channel fading model, closed-form expressions for the average outage probability (OP) and average bit error rate (BER) of the mixed dual-hop system are derived using the higher transcendental Meijer-G function. Similarly, the closed-form expression for the average ergodic capacity of the mixed relay system is obtained via the bivariate Fox-H function. Additionally, asymptotic performance analyses for the average outage probability and BER under high signal-to-noise ratio (SNR) conditions are provided. Finally, Monte Carlo simulations are conducted to validate the accuracy of the derived theoretical expressions and to illustrate the effects of key system parameters on the performance of the mixed relay FSO-UWOC system. Full article

Accelerated life tests are vital in reliability studies, especially as new technologies create highly reliable products to meet market demand and competition. Progressive stress accelerated life test (PSALT) allows continual stress adjustments. For reliability and survival analysis in accelerated life studies, generalized progressive hybrid censoring (GPHC) is very important. The research on GPHC in PSALT models is lacking despite its growing importance. Binomial elimination and generalized progressive hybrid censoring augment PSALT in this investigation. This research examines PSALT under the Generalized Kavya–Manoharan exponential distribution based on the GPHC scheme. Using gamma prior, maximum likelihood, and Bayesian techniques, estimate model parameters. Squared error and entropy loss functions yield Bayesian estimators using informational priors in simulation and non-informative priors in application. Various censoring schemes are calculated using Monte Carlo simulation. The methodology is demonstrated using two real-world accelerated life test data sets. Full article

Background: Foundational research on the gamma distribution and inventory control highlighted its flexibility and practicality for managing fast-moving finished goods. Nonetheless, concerns remain about conventional statistical approximations of lead-time demand (LTD) distributions. Real-world lead times often result in nonstandard LTD forms, and traditional methods may introduce parameter mismatches under nonclassical conditions. Despite these challenges, this research demonstrates that a gamma LTD approximation is an effective method for managing these goods. Methods: This study employs numerical experiments to assess accuracy at high service levels, focusing on errors in system cost and product availability. Three propositions are validated: (1) a standard distribution generally characterizes the demands of fast-moving items; (2) demand variability systematically modifies the form of nonstandard LTD distributions, enhancing accuracy; (3) nonclassical conditions generally improve the accuracy of properly parameterized gamma approximations. A purposive sample of disruptive lead-time distributions found in global maritime supply chains drives numerical experiments. Results: Externally validated evidence provides the following findings within our study context: (1) a nonstandard lead-time distribution does not necessarily result in a similar LTD distribution, as it also depends on demand variability; (2) demand variability positively affects the form of a nonstandard LTD distribution under conventional conditions, with nonclassical conditions enhancing this effect; (3) the shape transformations almost always improve the accuracy of a gamma approximation. Conclusions: A gamma LTD approximation can manage inventory for fast-moving finished goods effectively, even with disruptive lead times under both conventional and nonclassical conditions. Full article

In this study, we introduce a novel distribution related to the gamma distribution, referred to as the generalized incomplete gamma distribution. This new family is defined through a stochastic representation involving a linear transformation of a random variable following a distribution derived from the upper incomplete gamma function. As a result, the proposed distribution exhibits a probability density function that effectively captures data exhibiting asymmetry and both mild and high levels of kurtosis, providing greater flexibility compared to the conventional gamma distribution. We analyze the probability density function and explore fundamental properties, including moments, skewness, and kurtosis coefficients. Parameter estimation is conducted via the maximum likelihood method, and a Monte Carlo simulation study is performed to assess the asymptotic properties of the maximum likelihood estimators. To illustrate the applicability of the proposed distribution, we present two case studies involving real-world datasets related to mineral concentration and the length of odontoblasts in guinea pigs, demonstrating that the proposed distribution provides a superior fit compared to the gamma, inverse Gaussian, and slash-type distributions. Full article

This paper investigates the outage probability of a hybrid Radio Frequency–Underwater Wireless Optical Communication (RF-UWOC) system that employs the Decode-and-Forward protocol under composite fading channels. It is assumed that the RF link experiences Generalized K distribution fading along with atmospheric path loss, while the UWOC link endures generalized Gamma distribution turbulent fading, accounting for underwater path loss and pointing errors. Based on these assumptions, when intensity modulation with direct detection (IM/DD) and heterodyne detection (HD) are, respectively, utilized at the receiver, the average outage probability and its corresponding asymptotic expression for the considered hybrid dual-hop systems under high signal-to-noise ratios are derived. Subsequently, Monte Carlo simulations are conducted to validate the accuracy of the theoretical analysis results and to explore the influence of various key system parameters on the dual-hop systems. Full article