Continuous Distribution Research Articles

Enhancing apparel supply chain resilience: a robust-stochastic approach to integrated production-distribution planning

ABSTRACT This study focuses on designing a resilient supply chain for the apparel industry. We address the challenges of uncertain replenishment orders and production capacities in the apparel industry by developing a multi-objective robust two-stage stochastic programming model. The model optimizes total costs, customer service level, and financial risk. A continuous probability distribution is employed to model uncertainty, and downside risk is used as a risk measure. Computational results based on a real-world apparel company demonstrate the model’s effectiveness in enhancing supply chain resilience. By significantly reducing financial risk while maintaining acceptable cost levels, the proposed approach provides valuable insights for industry practitioners. In order to further analyze the impact of uncertain parameters on the planning problem’s performance, we carry out a sensitivity analysis. From a practical standpoint, the results highlight the effectiveness of the robust optimization model. The optimal solutions derived from the downside risk management approach show a substantial reduction in risk, with DRΩ decreasing by an impressive 83%. This significant risk mitigation is achieved with only a minimal increase in total costs, which remains under 4%. These findings emphasize the practical advantages of robust optimization, offering critical insights for researchers and practitioners to improve efficiency, reliability and financial stability in Supply Chain management.

The Mollified (Discrete) Uniform Distribution and Its Applications

ABSTRACTThe mollified uniform distribution is rediscovered, which constitutes a “soft” version of the continuous uniform distribution. Important stochastic properties are presented and used to demonstrate potential fields of applications. For example, it constitutes a model covering platykurtic, mesokurtic, and leptokurtic shapes. Its cumulative distribution function may also serve as the soft‐clipping response function for defining generalized linear models with approximately linear dependence. Furthermore, it might be considered for teaching, as an appealing example for the convolution of random variables. Finally, a discrete type of mollified uniform distribution is briefly discussed as well.

Applications of Ujlayan and Dixit Fractional Uniform Probability Distribution

In this work, we consider the Ujlayan-Dixit (UD) fractional derivative and integral to present the fractional probability density function for the Continuous Uniform Distribution (CUD). Some applications for this distribution using the UD approach are developed by introduce new fractional notions on the probability theory, which involve cumulative distribution, survival and hazard functions. For continuous random variables, various additional concepts and applications are established, including the fractional expectation, the fractional variance and the fractional moments. Finally, the UD fractional standard deviation and the UD fractional Shannon entropy are provided.

Impact of continuous distribution as the allocation strategy on lung transplantation.

In March 2023, the allocation strategy for lung transplantation (LT) underwent significant changes with the introduction of the new system, referred to as the continuous distribution (CD). The current paper describes the early impact of CD implementation on the mechanics of LT at a large tertiary care medical center. This was a retrospective study conducted across nine months before (March 2022 to November 2022) and after (March 2023 to November 2023) the implementation of the CD allocation system. The number of lung donor offers increased by 59% in the post-CD period (p=0.002). The median offers per waitlisted patient increased even more (p<0.001), leading to a significant reduction in time to transplant (p<0.001). Early clinical outcomes (median length of stay and hospital survival) were unchanged, while the cumulative length of index hospitalization was lower by 10% during the post-CD period. The cost/bed-day increased by 4.5% in a post-CD period, which converted to a 32% decrease in the contribution margin per transplant. In conclusion, the implementation of CD was associated with improved access to donor lungs, leading to favorable trends in the time to transplant while maintaining post-transplant outcomes. The CD was associated with a significant jump in the cost of LT.

Optimizing two-photon quantum scissor with imperfect detectors for continuous variable quantum key distribution

Optimizing two-photon quantum scissor with imperfect detectors for continuous variable quantum key distribution

A spatiotemporal autoregressive neural network interpolation method for discrete environmental factors

A spatiotemporal autoregressive neural network interpolation method for discrete environmental factors

ON THE LOMAX-UNIT TEISSIER DISTRIBUTION: PROPERTIES AND ITS APPLICATIONS

In this paper, a new modified continuous asymmetric probability distribution Lomax-Unit Teissier distribution (LxUTD) which extends the baseline Unit Teissier (UTD) distribution was developed. However, the new distribution is capable of handling an asymmetric data sets. Some statistical properties like moments, moment generating function, renyi entropy, quantile function, and order statistics was derived and presented theoretically. We also, proceed to test the validity of the new constructed continuous asymmetric probability distribution. A simulation was conducted to determine the efficiency of the estimated value by increasing the sample size. The result shows that when simulated or real life datasets are being used the new asymmetric probability distribution will give better fit than the competitive models.

An Extension of Some Truncated Distributions Family With Application

This paper represents a suggested a combination of continuous distributions based on Truncated Gompertz-G (tgo-gd[0,1]) and Truncated Gompertz-Weibull (tgo-wd) distributions. Some of the main properties of the suggested combination such as the distribution function (cdf), the probability function (pdf), survival function (Sf), hazard function (Hrf), quintile function (Qf), moment generating function (mgf), skewness ,, kurtosis , entropy, and maximum likelihood estimator (MLE) for the proposed combination of tgo-wd[0,1] have been presented. As well, an experimentally estimation for the parameters of the distributions using MLE have been studied. After the application, the potentiality of the proposed family by means of one real data sets are shown more flexibility in compare with the other models.

Spatial Evaluation of Salurnis marginella Occurrence According to Climate Change Using Multiple Species Distribution Models

Salurnis marginella causes agricultural and forest damage in various Asian environments. However, considering the environmental adaptability of pests and the active international trade, it may invade other regions in the future. As the damage to local communities caused by pests becomes difficult to control after invasion, it is essential to establish measures to minimize losses through pre-emptive monitoring and identification of high-risk areas, which can be achieved through model-based predictions. The aim of this study was to evaluate the potential distribution of S. marginella by developing multiple species distribution modeling (SDM) algorithms. Specifically, we developed the CLIMEX model and three machine learning-based models (MaxEnt, random forest, and multi-layer perceptron), integrated them to conservatively assess pest occurrence under current and future climates, and overlaid the host distribution with climatically suitable areas of S. marginella to identify high-risk areas vulnerable to the spread and invasion of the pest. The developed model, demonstrating a true skill statistic &gt;0.8, predicted the potential continuous distribution of the species across the southeastern United States, South America, and Central Africa. This distribution currently covers approximately 9.53% of the global land area; however, the model predicted this distribution would decrease to 6.85%. Possible areas of spread were identified in Asia and the southwestern United States, considering the host distribution. This study provides data for the proactive monitoring of pests by identifying areas where S. marginella can spread.

Significance of Morphology in Characterizing Human Health Risk from di(2-ethylhexyl) Phthalate in Polyvinyl Chloride Microplastics in Groundwater

In this study, a human health risk assessment was performed on the ingestion route of groundwater containing polyvinyl chloride (PVC) microplastics (MPs), and the carcinogenic and non-carcinogenic risks of di(2-ethylhexyl) phthalate (DEHP), a representative additive, were determined. In particular, the impact of volume diversity according to the shape (morphology) of PVC MP (fragment, fiber, film) on the risk characterization was intensively explored. Firstly, a continuous particle size distribution following a power function was derived using the abundance ratio of PVC MPs by size in the investigated groundwater, and human health risk assessment for DEHP in the PVC MPs was performed through the volume distribution according to the shape of MPs. DEHP human health risk assessment showed an excess cancer risk (ECR) of below 10−6 for a 95% cumulative probability for all MP shapes, but the values varied depending on the shape. Sensitivity analysis showed that the parameter that most affected human health risk was MP volume, second to concentration, which is dependent on MP shape. Therefore, it is necessary to consider the variety of MP shapes during human health risk assessment, and it can be achieved through probabilistic risk assessment utilizing the probability distribution for size and shape of MPs.

&lt;i&gt;Estimate the parameters of the ARMA model when the random error follows the two-parameter exponential distribution&lt;/i&gt;

This research deals with one of the types of models suggested by Box Jenkins, which is the ARMA (1,1) mixed model. Which can deal with time series, whether stable or unstable. The model was reviewed and its functions defined when the random error follows the abnormal distribution, and the exponential distribution with two parameters, which is a continuous distribution, was used. The appropriate tests were presented for the study and the parameters of the ARMA (1,1) model were estimated by the greatest possibility method. The parameters of the two-parameter exponential distribution were also estimated by the (MLS) method, and because the system did not have a solution even when using numerical methods, the moment method was resorted to. A set of real data representing wind speed in Iraq was analyzed, showing the appropriateness of the distribution of the data and verifying that the series is almost stable. In diagnosing the model, it was found that the proposed model is ARMA (1,1).

Modeling of lifetime scenarios with non-monotonic failure rates.

The Weibull distribution is an important continuous distribution that is cardinal in reliability analysis and lifetime modeling. On the other hand, it has several limitations for practical applications, such as modeling lifetime scenarios with non-monotonic failure rates. However, accurate modeling of non-monotonic failure rates is essential for achieving more accurate predictions, better risk management, and informed decision-making in various domains where reliability and longevity are critical factors. For this reason, we introduce a new three parameter lifetime distribution-the Modified Kies Weibull distribution (MKWD)-that is able to model lifetime scenarios with non-monotonic failure rates. We analyze the statistical features of the MKWD, such as the quantile function, median, moments, mean, variance, skewness, kurtosis, coefficient of variation, index of dispersion, moment generating function, incomplete moments, conditional moments, Bonferroni, Lorenz, and Zenga curves, and order statistics. Various measures of uncertainty for the MKWD such as Rényi entropy, exponential entropy, Havrda and Charvat entropy, Arimoto entropy, Tsallis entropy, extropy, weighted extropy and residual extropy are computed. We discuss eight different parameter estimation methods and conduct a Monte Carlo simulation study to evaluate the performance of these different estimators. The simulation results show that the maximum likelihood method leads to the best results. The effectiveness of the newly suggested model is demonstrated through the examination of two different sets of real data. Regression analysis utilizing survival times data demonstrates that the MKWD model offers a superior match compared to other current distributions and regression models.

On supergravity and noncritical strings

Motivated by the long-term goal of finding holographic descriptions for N = 1 and N = 2 super QCD, we revisit the subject of “noncritical” superstring theory. Focusing on string models with 6d super Poincaré invariance, we provide a careful worldsheet derivation of the leading-order effective theories for the lowest modes. We identify them as seven-dimensional, maximally supersymmetric gauged supergravities: the SO(4) theory for noncritical IIA and the ISO(4) theory for noncritical IIB. The same theories also arise as consistent truncations on S3 of the 10d IIB and IIA supergravities, respectively, where the chirality flip is as expected from T-duality. These effective supergravities should be interpreted in the following sense. The noncritical string can be viewed as a special case of a discrete series of backgrounds labelled by an integer k (which counts the number of NS5 branes in a certain duality frame); the “noncritical” value is k = 2, while for k → ∞ one recovers a weakly-curved 10d target space. The effective supergravities described here give an accurate description of the interactions among the lowest modes for k → ∞, with higher derivative corrections suppressed by powers of 1/k. We discuss BPS solutions of the 7d gauged supergravities and their uplift to 10d solutions. In particular, we find a novel class of solutions with RR flux, parametrized by a function of three variables that solves an elegant PDE. While we cannot solve the PDE in closed form except in trivial cases, we confirm that our solutions correspond to a 10d IIA Hanany-Witten setup with continuous distributions of both “color” D4 branes and “flavor” D6 branes.

Construction of a High-Density Genetic Linkage Map and QTL Mapping for Stem Rot Resistance in Passion Fruit (Passiflora edulis Sims).

The passion fruit (Passiflora edulis Sims) is a diploid plant (2n = 2x = 18) and is a perennial scrambling vine in Southern China. However, the occurrence and spread of stem rot in passion fruit severely impact its yield and quality. In this study, we re-sequenced a BC1F1 population consisting of 158 individuals using whole-genome resequencing. We constructed a high-density genetic linkage map and identified the quantitative trait locus (QTL), and analyzed candidate genes associated with stem rot resistance in passion fruit. Based on the passion fruit reference genome (MER), a high-density genetic linkage map was constructed with 1,180,406 single nucleotide polymorphisms (SNPs). The map contains nine linkage groups, covering a total genetic distance of 1559.03 cM, with an average genetic distance of 311.81 cM. The average genetic distance between 4206 bins was 0.404 cM, and the average gap length was 10.565 cM. The collinearity correlation coefficient between the genetic map and the passion fruit genome was 0.9994. Fusarium solani was used to infect the BC1F1 population, and the resistance to stem rot showed a continuous distribution. A QTL, qPSR5, was mapped to the 113,377,860 bp-114,811,870 bp genomic region on chromosome 5. We performed RNA sequencing (RNA-seq) and real-time quantitative polymerase chain reaction (RT-qPCR) to analyze the expression levels of predicted genes in the candidate region and identified ZX.05G0020740 and ZX.05G0020810 as ideal candidate genes for stem rot resistance in passion fruit. The findings in this study not only lay the foundation for cloning the qPSR5 responsible for stem rot resistance but also provide genetic resources for the genetic improvement of passion fruit.

An approach for parametric survival ANOVA with application to Weibull distribution

. Motivated by the serious Type-I error issues of widely used Cox-PH method in survival analysis, this article introduces an approach one can take in deriving superior parametric tests based on distributions such as the gamma, lognormal, and Weibull. Some of the data available from such distributions are allowed to be censored, as usually the case in dealing with lifetime distributions. Since the classical approach fails to provide reasonable procedures to test the equality of means of a number of Weibull populations, beyond the two populations case, we will show how to apply the generalized inference approach to do so in a novel manner. The approach should work in other scale invariant distributions, such as the gamma and lognormal. The approach is illustrated with the Weibull distributions, taking advantage of the fact that the original data from continuous distributions can be transformed into normally distributed data leading to exact generalized test variables.

A comparative study of interpolation methods for the development of ore distribution maps

Mining projects require precise knowledge about tonnage and quality of ore reserves for planning and decision-making. This is hard to establish as exploration operations, which are costly, time-consuming and require an accurate description of the deposit. Geologists use deterministic and geostatistical methods as interpolation tools to generate a continuous (or prediction) ore distribution map from known sampled data. A comparative study between four different geostatistical interpolation techniques: Ordinary Kriging (OK), Simple Kriging (SK), Universal Kriging (UK) and Empirical Bayesian Kriging (EBK); and four deterministic techniques: Inverse Distance Weighting (IDW), Global Polynomial Interpolation (GPI), Radial Basis Function (RBF), and Local Polynomial Interpolation (LPI) were applied. The 95% confidence level was measured and the effectiveness of each interpolation method was assessed through cross-validation for the construction of the corresponding maps displaying the distribution of ore on the surface with the use of GIS. The output methods are ranked to perform a comprehensive analysis using the error statistics methods: Mean Error (ME), Root Mean Square Error (RMSE), Mean Standardized Error (MSE) and Root Mean Square Standardized Error (RMSSE). The results show that GPI, EBK and Kriging methods perform the best results while IDW has good statistical analysis factors but it came in the tail of the rank. Therefore, there is no appropriate interpolation method accurate for all cases, each method must be statistically evaluated before each application and essentially based on real data.

A New Truncated Family of Log Logistic Distribution

Compound probability models have important roles in modeling real life events, in this paper, a new class of continuous distributions was presented named Truncated [0,1] Log logistic -Log logistic distribution ([0,1] TLL-LLD). And we presented the important properties of the new distribution model, which are the r-th moment function, reliability function, the function of hazard, the function stress strength function , and the function of Shannon entropy.

Improving the Prioritization of Heart Transplantation Candidates for Optimal Clinical Outcomes: A Narrative Review.

This narrative review evaluates the limitations of current heart transplantation allocation models, which prioritize medical urgency and waitlist time but fail to adequately predict long-term post-transplant outcomes. It aims to identify advanced metrics that can strengthen the prioritization framework while addressing persistent racial, geographic, and socioeconomic inequities in access to transplantation. Recent research indicates that incorporating frailty, nutritional status, immunological compatibility, and pulmonary hemodynamics into allocation frameworks can enhance the prediction of transplant outcomes. The growing use of mechanical circulatory support (MCS) as a bridge to transplantation provides stabilization for critically ill patients; however, disparities in access persist. Studies continue to emphasize the barriers faced by minority and pediatric populations, highlighting the need for expanded donor networks and improved matching criteria. This review highlights the necessity of shifting transplantation prioritization toward multidimensional candidate evaluations that consider both clinical complexity and long-term outcomes. Policy reforms aimed at addressing healthcare disparities and optimizing donor utilization are crucial for improving patient outcomes. Future research should focus on assessing the effectiveness of advanced allocation models, such as continuous distribution frameworks, to promote equitable and sustainable transplantation systems.

Towards the sustainability of African sandalwood: Understanding the distribution and environmental requirements

Societal Impact StatementAfrican sandalwood (Osyris lanceolata) leaves, roots, barks, fruits, and woods are used for multiple purposes throughout Asia, Africa, and Europe. The species is threatened in several eastern African countries. To improve the species' management and conservation, a habitat suitability study was undertaken in its at‐risk region in eastern Africa and extended to southern and horn of Africa due to its continuous distribution. African sandalwood continues to face intense human pressure and needs to be prioritized in terms of sustainable management practices. The plant's significant human importance necessitates inclusive conservation measures in all three habitat regions in Africa to safeguard it.Summary African sandalwood (Osyris lanceolata) is a versatile plant with significant economic and societal importance. It is threatened in several countries in Africa due to overexploitation. The lack of knowledge about the plant's ecology and environmental requirements complicates the species' long‐term management. We sought to address this issue by providing a novel understanding of the environmental factors that influence the occurrence of African sandalwood and its potential distribution. Using publicly available occurrence records from 1950 to 2021 and field data, we examined the species' habitat requirements in eastern, southern, and horn of Africa regions. We applied the Generalized Additive Models to link the plant's occurrence data to 12 environmental variables reflecting climatic, physiographic, and edaphic characteristics, while controlling for the biases that arise from publicly gathered occurrence records. Our findings revealed that the plant's habitat requirements vary among the three regions investigated. While climatic factors are essential in all three regions, physiographic aspects are mainly important for the eastern and southern populations, while edaphic variables were pertinent exclusively in southern region. Areas suitable and optimal for the plant were estimated to comprise 674,700 km2 (17.3% of total land area) in eastern Africa, 267,750 km2 (25.6%) in the horn of Africa, and 716,300 km2 (13.9%) in southern Africa. More than two‐thirds of these areas are located on unprotected lands, highlighting the importance of community involvement for a sustainable management of the species. Our results on the potential geographical distribution of African sandalwood are crucial to guide more targeted conservation and recovery efforts.

Distribution of volumes of plasma channels components between metal granules in working liquids

Introduction. Expanding the capabilities of a number of modern technologies and improving quality of their products require detailed spark and plasma erosion processes control in metal granules layers (MGL). Problem. Traditional measurement of exclusively electrical parameters of these processes, even in the case of multi-electrode systems, provides only a general vision, not allowing monitoring processes in individual plasma channels. Optical control methods make it possible to simultaneously have information about almost every plasma channel in the MGL. The aim of the article is to study the characteristic components of plasma channels arising as a result of the flow of discharge currents in the MGL and to establish the laws of distribution of their volumes and their ratios. Methodology. During the experiments, photographs of plasma channels resulting from the flow of discharge current pulses between Al granules immersed in distilled water were obtained. Using the specialized ToupView program, the volumes of equivalent ellipsoids of rotation, approximating the colored halos and white cores of the plasma channels were determined. Discrete distributions of the volumes of the halo and cores of plasma channels, as well as their ratios were constructed both with and without procedures for screening out «anomalous» results. The efficiency of approximation of discrete distributions obtained in practice by continuous theoretical distributions Weibull, Rosin-Rammler and log-normal was estimated. Results. It is shown that of all the considered theoretical distributions of halo and cores of plasma channels volumes, as well as their ratios, the most adequate is the log-normal one. Originality. For the first time distributions of volumes of halo and cores of plasma channels were studied and their comparative analysis with the size distributions of erosion particles and dimples on the surface of Al granules was given. Practical significance. Taking into account the new obtained results, a technique for constructing distributions of volumes of halo and cores of plasma channels and determining their parameters has been developed. References 53, figures 7, tables 5.