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Upon researching predictive models related to West Nile virus disease, it is discovered that there are numerous parameters and extensive information in most models, thus contributing to unnecessary complexity. Another challenge frequently encountered is the lead time, which refers to the period for which predictions are made and often is too short. This paper addresses these issues by introducing a parsimonious method based on ICC curves, offering a logistic distribution model derived from the vector-borne SEIR model. Unlike existing models relying on diverse environmental data, our approach exclusively utilizes historical and present infected human cases (number of new cases). With a year-long lead time, the predictions extend throughout the 12 months, gaining precision as new data emerge. Theoretical conditions are derived to minimize Bayesian loss, enhancing predictive precision. We construct a Bayesian forecasting probability density function using carefully selected prior distributions. Applying these functions, we predict month-specific infections nationwide, rigorously evaluating accuracy with probabilistic metrics. Additionally, HPD credible intervals at 90%, 95%, and 99% levels is performed. Precision assessment is conducted for HPD intervals, measuring the proportion of intervals that does not include actual reported cases for 2020–2022.

Upon researching predictive models related toWest Nile virus disease, it is discovered that there are numerous parameters and extensive information in most models, thus contributing to unnecessary complexity. Another challenge frequently encountered is the lead time, which refers to the period for which predictions are made and often is too short. This paper addresses these issues by introducing a parsimonious method based on ICC curves, offering a logistic distribution model derived from the vector-borne SEIR model. Unlike existing models relying on diverse environmental data, our approach exclusively utilizes historical and present infected human cases (number of new cases). With a yearlong lead time, the predictions extend throughout the 12 months, gaining precision as new data emerge. Theoretical conditions are derived to minimize Bayesian loss, enhancing predictive precision. We construct a Bayesian forecasting probability density function using carefully selected prior distributions. Applying these functions, we predict monthspecific infections nationwide, rigorously evaluating accuracy with probabilistic metrics. Additionally, HPD credible intervals at 90%, 95%, and 99% levels is performed. Precision assessment is conducted for HPD intervals, measuring the proportion of intervals that does not include actual reported cases for 2020e2022. [ABSTRACT FROM AUTHOR]

This work proposes a wavelet shrinkage rule under asymmetric LINEX loss function and a mixture of a point mass function at zero and the logistic distribution as prior distribution to the wavelet coefficients in a nonparametric regression model with gaussian error. Underestimation of a significant wavelet coefficient can lead to the bad detection of features of the unknown function, such as peaks, discontinuities, and oscillations. It can also occur under asymmetrically distributed wavelet coefficients. Thus, the proposed rule is suitable when overestimation and underestimation have asymmetric losses. Statistical properties of the rule, such as squared bias, variance, frequentist, and bayesian risks, are obtained. Simulation studies are conducted to evaluate the performance of the rule against standard methods and an application in a real dataset involving infrared spectra is provided.

The Black–Scholes model and many of its extensions imply a log-normal distribution of stock total returns over any finite holding period. However, for a holding period of up to one year, empirical stock return distributions (both conditional and unconditional) are not log-normal, but rather much closer to the logistic distribution. This paper derives analytic option pricing formulas for an underlying asset with a logistic return distribution. These formulas are simple and elegant and employ exactly the same parameters as B&S. The logistic option pricing formula fits empirical option prices much better than B&S, providing explanatory power comparable to much more complex models with a larger number of parameters. [ABSTRACT FROM AUTHOR]

The study and investigation of the behavior of monetary phenomena is an interesting subject for actuaries and practitioners. In the recent age and development in the monetary and financial phenomena, cryptocurrency has gained much attention from actuaries. Over the past decade, several research studies have emerged on modeling and forecasting cryptocurrency exchange rates. This paper also contributes to the modeling of cryptocurrency exchange rates using a new version of the Logistic distribution, namely, a new cotangent-Logistic distribution. The mathematical properties and estimators of the new cotangent-logistic distribution's parameters are obtained. We illustrate the new cotangent-Logistic distribution using two financial data sets representing the log-returns of the Bitcoin and Ethereum prices. We compare the new cotangent-Logistic distribution with the baseline Logistic distribution and its modified version. Using the p-value and three other statistical tests, we show that the new cotangent-Logistic distribution repeatedly provides the optimal fit to cryptocurrency exchange rates.

The study and investigation of the behavior of monetary phenomena is an interesting subject for actuaries and practitioners. In the recent age and development in the monetary and financial phenomena, cryptocurrency has gained much attention from actuaries. Over the past decade, several research studies have emerged on modeling and forecasting cryptocurrency exchange rates. This paper also contributes to the modeling of cryptocurrency exchange rates using a new version of the Logistic distribution, namely, a new cotangent-Logistic distribution. The mathematical properties and estimators of the new cotangent-logistic distribution's parameters are obtained. We illustrate the new cotangent-Logistic distribution using two financial data sets representing the log-returns of the Bitcoin and Ethereum prices. We compare the new cotangent-Logistic distribution with the baseline Logistic distribution and its modified version. Using the p-value and three other statistical tests, we show that the new cotangent-Logistic distribution repeatedly provides the optimal fit to cryptocurrency exchange rates. [ABSTRACT FROM AUTHOR]

We investigate the cumulative Tsallis entropy, an information measure recently introduced as a cumulative version of the classical Tsallis differential entropy, which is itself a generalization of the Boltzmann-Gibbs statistics. This functional is here considered as a perturbation of the expected mean residual life via some power weight function. This point of view leads to the introduction of the dual cumulative Tsallis entropy and of two families of coherent risk measures generalizing those built on mean residual life. We characterize the finiteness of the cumulative Tsallis entropy in terms of L p -spaces and show how they determine the underlying distribution. The range of the functional is exactly described under various constraints, with optimal bounds improving on all those previously available in the literature. Whereas the maximization of the Tsallis differential entropy gives rise to the classical q -Gaussian distribution which is a generalization of the Gaussian having a finite range or heavy tails, the maximization of the cumulative Tsallis entropy leads to an analogous perturbation of the Logistic distribution. [ABSTRACT FROM AUTHOR]

In this paper, a simplified method aimed at generating ground motions records using a Fourier amplitude spectrum model obtained by a response spectrum is presented. The use of white noise with specific conditions on the variance and inter‐frequency correlation allows to get a realistic variability of the Fourier amplitude spectrum. Moreover, a two‐corner frequency model is defined from empirical ground‐motion data and a filter is applied to capture the attenuation at high frequencies. The generated series of stochastic ground motions accurately match the mean value of the target response spectrum. The procedure was tested on an Italian site and results showed excellent matching in terms of mean and dispersion values with either the median obtained from ground motion prediction equations (GMPE) and conditional mean spectra (CMS). The advantage of the proposed methodology is that time‐histories can be generated with low computational effort, they do not need scaling or frequency content adjustments and are spectrum compatible with a given target spectrum. [ABSTRACT FROM AUTHOR]

We propose a new class of goodness‐of‐fit tests for the logistic distribution based on a characterization related to the density approach in the context of Stein's method. This characterization‐based test is a first of its kind for the logistic distribution. The asymptotic null distribution of the test statistic is derived and it is shown that the test is consistent against fixed alternatives. The finite sample power performance of the newly proposed class of tests is compared to various existing tests by means of a Monte Carlo study. It is found that this new class of tests are especially powerful when the alternative distributions are heavy tailed, like Student's t and Cauchy, or for skew alternatives such as the log‐normal, gamma and chi‐square distributions. [ABSTRACT FROM AUTHOR]

Statistical data analysis available in most scientific fields is often recorded with measurement error. The modeling of these statistical data by ignoring the measurement errors, leads to estimators of the parameters of the distributions, whose use does not achieve sufficient accuracy in the goodness of fit. In reliability criteria, one of the important issues is hazard rate function. It prompted us to investigate the hazard rate criterion in the presence of measurement error generated from the normal or logistic distribution. Now, while providing the estimator for the density function using local time polynomial estimator methods, the risk rate function is estimated according to the contamination degree of 15 or 30%. Finally, we present the numerical analysis.

A new set of ordered random variables generated from a sample from a scale dependent Cauchy distribution known as Absolved Order Statistics (AOS) of the sample forms the problem of investigation in this paper. The distribution theory of these AOS has been developed. The vector of AOS is found to be the minimal sufficient statistic for the Cauchy distribution which is contrary to the existing perception that the vector of order statistics of the sample is minimal sufficient. The best linear unbiased estimate ˆσ of σ based on AOS is derived and its variance is also explicitly expressed. Though only n−4 intermediate order statistics are usable to determine the BLUE of σ based on order statistics, it is found that n−2 AOS are usable to determine ˆσ. This makes ˆσ more efficient estimate of σ than all of its competitors especially when the sample size is small. Illustration for the above result is made through a real life example. It is found that censoring based on AOS is more realistic and the estimate obtained from it for σ is more efficient than the case of censoring with order statistics. A new ranked set sampling known as Adjusted Ranked Set Sampling which is suitable for Cauchy distribution and results with observations distributed as AOS is developed in this paper. Further its role in producing better estimate for σ is analyzed.

Abstract In this paper, a new three-parameter distribution, which is a member of the Alpha Power Transformed Family of distributions, is introduced. The new distribution is a generalization of the logistic model called the alpha power transformed logistic (APTL) distribution. Some mathematical properties of the new distribution like moments, quantile function, median, skewness, kurtosis, Rényi entropy, and order statistics are discussed. The parameters of the distribution are estimated using the maximum likelihood estimation method and a simulation study is performed to investigate the effectiveness of the estimates. The usefulness and flexibility of the APTL distribution in modelling financial data are investigated using two portfolio stock indices, namely the NASDAQ and New York stock indices, both from the United States stock market. Based on the model selection criteria, we are able to establish empirically that the APTL distribution is the best for modelling the two data sets, among the various distributions compared in the study. For each of the data, the quantile value-at-risk estimates for the APTL distribution give the smaller expected portfolio loss at high confidence levels in comparison to those of the other distributions. Keywords: Alpha power transformed family of distributions; logistic distribution; maximum likelihood estimation; portfolio investments; value-at-risk. Abstrak Pada artikel ini, diperkenalkan distribusi baru dengan tiga parameter yang merupakan anggota dari keluarga distribusi Alpha Power Transformed. Distribusi baru ini merupakan generalisasi dari model logistik yang disebut distribusi Alpha Power Transform Logistics (APTL). Selain itu, dibahas pula beberapa sifat matematika dari distribusi tersebut yaitu momen, fungsi kuantil, median, kemiringan, kurtosis, entropi Rényi, dan statistik terurut. Parameter distribusi diestimasi menggunakan metode maximum likelihood estimation dan studi simulasi dilakukan untuk menyelidiki keefektifan estimasi. Kegunaan dan fleksibilitas distribusi APTL dalam pemodelan data keuangan diselidiki menggunakan dua indeks saham portofolio dari pasar saham Amerika Serikat yaitu indeks saham NASDAQ dan New York. Berdasarkan kriteria pemilihan model, secara empiris, dihasilkan bahwa APTL adalah distribusi terbaik untuk memodelkan dua set data di antara berbagai distribusi yang dibandingkan pada penelitian ini. Untuk setiap data, estimasi kuantil value-at-risk untuk distribusi APTL memberikan kerugian portofolio yang diharapkan lebih kecil dengan tingkat kepercayaan tinggi dibandingkan dengan distribusi lainnya. Kata Kunci: distribusi dari keluarga Alpha power transformed; distribusi logistik; maximum likelihood estimation; investasi portofolio; value-at-risk. 2020MSC: 62E10.

The COVID-19 epidemic has had a profound effect on almost every aspect of daily life, including the financial sector, education, transportation, health care, and so on. Among these sectors, the financial and health sectors are the most affected areas by COVID-19. Modeling and predicting the impact of the COVID-19 epidemic on the financial and health care sectors is particularly important these days. Therefore, this paper has two aims, (i) to introduce a new probability distribution for modeling the financial data set (oil prices data), and (ii) to implement a machine learning approach to predict the oil prices. First, we introduce a new approach for developing new probability distributions for the univariate analysis of the oil price data. The proposed approach is called a new reduced exponential-$ X $ (NRE-$ X $) family. Based on this approach, two new statistical distributions are introduced for modeling the oil price data and its log returns. Based on certain statistical tools, we observe that the proposed probability distributions are the best competitors for modeling the prices' data sets. Second, we carry out a multivariate analysis while considering some covariates of oil price data. Dual well-known machine learning algorithms, namely, the least absolute shrinkage and absolute deviation (Lasso) and Elastic net (Enet) are utilized to achieve the important features for oil prices based on the best model. The best model is established through forecasting performance.

Abstract Tests for the goodness of fit of logistic distribution have received much attention in the literature as it is widely used in many studies related to bio-assay, population growth, etc. In this paper, we propose a method to test whether the data comes from a logistic distribution or not. We derive the asymptotic distribution of the test statistic. Also, we develop a test based on Jackknife Empirical Likelihood (JEL). The finite sample performance of the JEL ratio test is evaluated through Monte Carlo simulation. We illustrate the proposed method using a real data set. [ABSTRACT FROM AUTHOR]

In existing studies, it has been argued that factor analysis (FA) is equivalent to item response theory (IRT) and that IRT models that use different functions (i.e., logistic and normal ogive) are also interchangeable. However, these arguments have weak links. The proof of equivalence between FA and normal ogive IRT assumes a normal distribution. The interchangeability between the logistic and normal ogive IRT models depends on a scaling constant, but few scholars have examined whether the usual values of 1.7 or 1.702 maximize interchangeability. This study addresses these issues through Monte Carlo simulations. First, the FA model produces almost identical results to those of the normal ogive model even under severe nonnormality. Second, no single scaling constant maximizes the interchangeability between logistic and normal ogive models. Instead, users should choose different scaling constants depending on their purpose in using a model and the number of response categories (i.e., dichotomous or polytomous). Third, the interchangeability between logistic and normal ogive models is determined by several conditions. The interchangeability is high if the data are dichotomous or if the latent variables follow a symmetric distribution, and vice versa. In summary, the interchangeability between FA and normal ogive models is greater than expected, but that between logistic and normal ogive models is not. [ABSTRACT FROM AUTHOR]

In this paper, we derive the L-moments for some distributions, such as logistic, generalized logistic, doubly truncated logistic, and doubly truncated generalized logistic distributions. We also establish some new axioms and identities, including recurrence relations satisfied by the L-moment from the underlying derivations. In addition, we establish some new general recurrence relations satisfied by the L-moment from any distribution. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Industrial Engineering Research in Production Systems is the property of Bu-Ali Sina University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The quest for energy efficiency in buildings has placed a demand for designing and modeling energy-efficient buildings. In this study, the thermal energy performance of a tropically adapted passive building was investigated in the warm tropical climate of Malaysia. Two mock-up buildings were built to represent a "green", made of clay brick double-glazed passive building and a conventional, made of concrete "red" building. The mean indoor temperature of the passive building was found to be always lower than that of the red building throughout the experiment during different weather constellations. Our research builds upon existing work in the field by combining multiple linear regression models and distribution models to provide a comprehensive analysis of the factors affecting the indoor temperature of a building. The results from the fitted multiple linear regression models indicate that walls and windows are critical components that considerably influence the indoor temperature of both passive buildings and red buildings, with the exception of passive buildings during the hot season, where the roof has a greater influence than the window. Furthermore, the goodness-of-fit test results of the mean indoor temperature revealed that the Fréchet and Logistic probability models fitted the experimental data in both cold and hot seasons. It is intended that the findings of this study would help tropical countries to devise comfortable, cost-effective passive buildings that are green and energy efficient to mitigate global warming. [ABSTRACT FROM AUTHOR]

Large-scale irrigation area water-saving renovation projects have large investment and many influencing factors. In order to objectively evaluate the implementation effect of large-scale irrigation area water-saving renovation projects, it is necessary to judge whether the renovation goals are achieved. This paper selected 25 evaluation indicators from four aspects of project construction, water-saving and incomeincreasing benefits, irrigation area management reform and irrigation area sustainable development, put forward 4-level classification standards and methods and established a large-scale irrigation area water-saving renovation project implementation effect evaluation system. The membership function was determined by logistic distribution, the maximum membership method was improved and a fuzzy comprehensive evaluation method for the implementation effect of large-scale irrigation area water-saving renovation projects based on logistic distribution was proposed. Taking a large-scale irrigation area in Hebei Province as an example to conduct an example evaluation, it is concluded that the comprehensive membership degree of the implementation effect of the water-saving renovation project in this irrigation area is 0.573 0 and the overall evaluation is good (II). The evaluation results are basically consistent with the actual situation of the implementation of the watersaving renovation project in the irrigation area. [ABSTRACT FROM AUTHOR]

The COVID-19 epidemic has had a profound effect on almost every aspect of daily life, including the financial sector, education, transportation, health care, and so on. Among these sectors, the financial and health sectors are the most affected areas by COVID-19. Modeling and predicting the impact of the COVID-19 epidemic on the financial and health care sectors is particularly important these days. Therefore, this paper has two aims, (i) to introduce a new probability distribution for modeling the financial data set (oil prices data), and (ii) to implement a machine learning approach to predict the oil prices. First, we introduce a new approach for developing new probability distributions for the univariate analysis of the oil price data. The proposed approach is called a new reduced exponential- (NRE- ) family. Based on this approach, two new statistical distributions are introduced for modeling the oil price data and its log returns. Based on certain statistical tools, we observe that the proposed probability distributions are the best competitors for modeling the prices' data sets. Second, we carry out a multivariate analysis while considering some covariates of oil price data. Dual well-known machine learning algorithms, namely, the least absolute shrinkage and absolute deviation (Lasso) and Elastic net (Enet) are utilized to achieve the important features for oil prices based on the best model. The best model is established through forecasting performance. [ABSTRACT FROM AUTHOR]

In existing studies, it has been argued that factor analysis (FA) is equivalent to item response theory (IRT) and that IRT models that use different functions (i.e., logistic and normal ogive) are also interchangeable. However, these arguments have weak links. The proof of equivalence between FA and normal ogive IRT assumes a normal distribution. The interchangeability between the logistic and normal ogive IRT models depends on a scaling constant, but few scholars have examined whether the usual values of 1.7 or 1.702 maximize interchangeability. This study addresses these issues through Monte Carlo simulations. First, the FA model produces almost identical results to those of the normal ogive model even under severe nonnormality. Second, no single scaling constant maximizes the interchangeability between logistic and normal ogive models. Instead, users should choose different scaling constants depending on their purpose in using a model and the number of response categories (i.e., dichotomous or polytomous). Third, the interchangeability between logistic and normal ogive models is determined by several conditions. The interchangeability is high if the data are dichotomous or if the latent variables follow a symmetric distribution, and vice versa. In summary, the interchangeability between FA and normal ogive models is greater than expected, but that between logistic and normal ogive models is not.

This paper addresses the optimal stochastic allocation of distributed energy resources in distribution networks. Typically, uncertain problems are analyzed in multistage formulations, including case generation routines, resulting in computationally exhaustive programs. In this article, two probabilistic approaches are proposed–range probability optimization (RPO) and value probability optimization (VPO)–resulting in a single-stage, convex, stochastic optimal power flow problem. RPO maximizes probabilities within a range of uncertainty, whilst VPO optimizes the values of random variables and maximizes their probabilities. Random variables were modeled with hourly measurements fitted to the logistic distribution. These formulations were tested on two systems and compared against the deterministic case built from expected values. The results indicate that assuming deterministic conditions ends in highly underestimated losses. RPO showed that by including ±10% uncertainty, losses can be increased up to 40% with up to −72% photovoltaic capacity, depending on the system, whereas VPO resulted in up to 85% increases in power losses despite PV installations, with 20% greater probabilities on average. By implementing any of the proposed approaches, it was possible to obtain more probable upper envelopes in the objective, avoiding case generation stages and heuristic methods. [ABSTRACT FROM AUTHOR]

This paper considers a new family of the trimodal skew logistic distributions. Some properties of this distribution, including moments, moments generating function, entropy, maximum likelihood estimates of parameters and some other properties, are presented. A simulation study is conducted to examine the performance of the parameters. Numerical optimization is carried out via two real-life datasets. Results show that the new distribution is better fitted in terms of these datasets among logistic, skew logistic and alpha skew logistic distributions based on the value of AIC and BIC. [ABSTRACT FROM AUTHOR]

Copyright of Nonferrous Metals (Mining Section) is the property of Beijing Research Institute of Mining & Metallurgy Technology Group and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In parametric statistical modeling, it is important to construct new extensions of existing probability distributions (PDs) that can make modeling data more flexible and help stakeholders make better decisions. In the present study, a new family of probability distributions (FPDs) called the odd beta prime generalized (OBP-G) FPDs is proposed to improve the traditional PDs. A new PD called the odd beta prime-logistic (OBP-logistic) distribution has been developed based on the developed OBP-G FPDs. Some desirable mathematical properties of the proposed OBP-logistic distribution, including the moments, moment-generating function, information-generating function, quantile function, stress–strength, order statistics, and entropies, are studied and derived. The proposed OBP-logistic distribution's parameters are determined by adopting the maximum likelihood estimation (MLE) method. The applicability of the new PD was demonstrated by employing three data sets and these were compared by the known extended logistic distributions, such as the gamma generalized logistic distribution, new modified exponential logistic distribution, gamma-logistic distribution, exponential modified Weibull logistic distribution, exponentiated Weibull logistic distribution, and transmuted Weibull logistic distribution. The findings reveal that the studied distribution provides better results than the competing PDs. The empirical results showed that the new OBP-logistic distribution performs better than the other PDs based on several statistical metrics. We hoped that the newly constructed OBP-logistic distribution would be an alternative to other well-known extended logistic distributions for the statistical modeling of symmetric and skewed data sets. [ABSTRACT FROM AUTHOR]

Cryptocurrency is a digital currency and also exists in the form of coins. It has turned out as a leading method for peer-to-peer online cash systems. Due to the importance and increasing influence of Bitcoin on business and other related sectors, it is very crucial to model or predict its behavior. Therefore, in recent, numerous researchers have attempted to understand and model the behaviors of cryptocurrency exchange rates. In the practice of actuarial and financial studies, heavy-tailed distributions play a fruitful role in modeling and describing the log returns of financial phenomena. In this paper, we propose a new family of distributions that possess heavy-tailed characteristics. Based on the proposed approach, a modified version of the logistic distribution, namely, a new modified exponential-logistic distribution is introduced. To illustrate the new modified exponential-logistic model, two financial data sets are analyzed. The first data set represents the log-returns of the Bitcoin exchange rates. Whereas, the second data set represents the log-returns of the Ethereum exchange rates. Furthermore, to forecast the high volatile behavior of the same datasets, we apply dual machine learning algorithms, namely Artificial neural network and support vector regression. The effectiveness of these models is evaluated against self exciting threshold autoregressive model.

Logistics distribution problems in responding to disasters have triggered numerous studies on humanitarian logistics (HL) and humanitarian supply chain management (HSCM). This is indicated by the growing number of publications on the topic every year. However, thematic literature reviews on humanitarian logistics and supply chain management (HLSCM) in natural disaster management are barely available. Therefore, this article proposes a sequential thematic literature review method to extensively review HLSCM publications to identify gaps and future research directions. The Scopus and Web of Science (WoS) databases have been used to obtain influential articles published between 2001 and 2021. The literature review found that distribution delay, demand uncertainty, and high operation costs are primary logistics distribution problems for disaster management. Therefore, theme determination was carried out using a problem-cause-solution order to solve these problems. Then, five specific themes of HLSCM were grouped namely (i) lean and agile, (ii) information technology and information science, (iii) modeling and simulation, (iv) determining and mitigating risk, and (v) management inventory. Finally, in terms of future research direction, there is a possibility for this study to be used as a reference for further studies on HLSCM. [ABSTRACT FROM AUTHOR]

A new two-parameter distribution is defined for modeling non-monotone lifetime data. It is constructed based on the logistic-G family and the exponential distribution. Its hazard rate properties are different than those of the well-known distributions. Some of its statistical properties are presented. An extended regression based on the logarithm of the random variable of the introduced distribution is defined. The new regression can provide better fits than other special regressions for analyzing real data. The performance of the maximum likelihood estimates is investigated from a simulation study. Three lifetime data sets are used to prove empirically the usefulness of the new models.

The concept of extended slash distribution is introduced. For the extended slash distribution of the sum of two independent logistic random variables, the characteristic function, moments, absolute moments and conditional tail expectation are obtained. It is shown that this distribution is related to the logistic and the generalized hyperbolic secant distributions by means of several distributional identities. The log-concavity of the distribution is studied. The self-decomposability of this distribution is also proved. Finally, an asymmetric distribution based on the extended slash distribution of the sum of two independent logistic random variables is introduced. Closed form expressions for the moments and for the conditional tail expectation of this skewed distribution are obtained. This distribution is a fairly flexible model for leptokurtic data as can be seen by fitting it to several datasets. [ABSTRACT FROM AUTHOR]

In the manufacturing industry, process surveillance plays an important role in improving product reliability. Many monitoring procedures have been devised to improve the reliability of a product in the literature. Due to cascading nature of multistage processes, the quality variable of the final stage can be influenced by the quality variable in the previous stages. Furthermore, the ordinary least squares method produces biased estimates if there are outliers in the historical data. The existence of cascade property in the multistage process and the presence of influential observations (outliers) in the historical data make the analysis of control schemes more challenging. Therefore, it is essential to take into account the impact of effective covariates and outliers in the historical dataset. In this paper, a cumulative sum (CUSUM) and two exponentially weighted moving average (EWMA) charts have been developed to monitor a two‐stage‐dependent process. The proportional hazard (PH) model has been applied to model the relationship among the incoming and outgoing variables of the two stage process. To deal with the deleterious effects of outliers on the results, a robust regression technique known as the M‐estimation has been implemented and the performance of the proposed monitoring procedures has been analyzed through Monte Carlo simulations. Lastly, two real‐life applications of the proposed control schemes are presented. [ABSTRACT FROM AUTHOR]

In modern Reinforcement Learning (RL) approaches, optimizing the Bellman error is a critical element across various algorithms, notably in deep Q-Learning and related methodologies. Traditional approaches predominantly employ the mean-squared Bellman error (MSELoss) as the standard loss function. However, the assumption of Bellman errors following the Gaussian distribution may oversimplify the nuanced characteristics of RL applications. In this work, we revisit the distribution of Bellman error in RL training, demonstrating that it tends to follow the Logistic distribution rather than the commonly assumed Normal distribution. We propose replacing MSELoss with a Logistic maximum likelihood function (LLoss) and rigorously test this hypothesis through extensive numerical experiments across diverse online and offline RL environments. Our findings consistently show that integrating the Logistic correction into the loss functions of various baseline RL methods leads to superior performance compared to their MSE counterparts. Additionally, we employ Kolmogorov–Smirnov tests to substantiate that the Logistic distribution offers a more accurate fit for approximating Bellman errors. This study also offers a novel theoretical contribution by establishing a clear connection between the distribution of Bellman error and the practice of proportional reward scaling, a common technique for performance enhancement in RL. Moreover, we explore the sample-accuracy trade-off involved in approximating the Logistic distribution, leveraging the Bias–Variance decomposition to mitigate excessive computational resources. The theoretical and empirical insights presented in this study lay a significant foundation for future research, potentially advancing methodologies, and understanding in RL, particularly in the distribution-based optimization of Bellman error. • We challenge the belief in a Normally distributed Bellman error with a Logistic distribution. • We explore Logistic distribution sampling error using Bias-Variance decomposition for optimal batch size. • We confirm the Logistic distribution's robustness for Bellman error with extensive testing and Kolmogorov–Smirnov tests. Novelty : We provide the first rigorous Logistic distribution modeling scheme for modeling the distribution of Bellman error and relate it to the reward scaling problem. [ABSTRACT FROM AUTHOR]

In this paper, we derive the L-moments for some distributions, such as logistic, generalized logistic, doubly truncated logistic, and doubly truncated generalized logistic distributions. We also establish some new axioms and identities, including recurrence relations satisfied by the L-moment from the underlying derivations. In addition, we establish some new general recurrence relations satisfied by the L-moment from any distribution.

In Basel III, the credit valuation adjustment (CVA) was given, and it was discussed that a bank covers mark-to-market losses for expected counterparty risk with a CVA capital charge. The purpose of this study is threefold. Using the logistic distribution, it is shown how the expected exposure can be derived for an interest rate swap. Secondly, the risk measure of VaR is contributed for the CVA under this distribution. Thirdly, generalizations for the CVA VaR and CVA CVaR are given by considering both the credit spread and the expected positive exposure to follow the logistic distributions with different parameters. Finally, several simulations are provided to uphold the theoretical discussions. [ABSTRACT FROM AUTHOR]

Cryptocurrency is a digital currency and also exists in the form of coins. It has turned out as a leading method for peer-to-peer online cash systems. Due to the importance and increasing influence of Bitcoin on business and other related sectors, it is very crucial to model or predict its behavior. Therefore, in recent, numerous researchers have attempted to understand and model the behaviors of cryptocurrency exchange rates. In the practice of actuarial and financial studies, heavy-tailed distributions play a fruitful role in modeling and describing the log returns of financial phenomena. In this paper, we propose a new family of distributions that possess heavy-tailed characteristics. Based on the proposed approach, a modified version of the logistic distribution, namely, a new modified exponential-logistic distribution is introduced. To illustrate the new modified exponential-logistic model, two financial data sets are analyzed. The first data set represents the log-returns of the Bitcoin exchange rates. Whereas, the second data set represents the log-returns of the Ethereum exchange rates. Furthermore, to forecast the high volatile behavior of the same datasets, we apply dual machine learning algorithms, namely Artificial neural network and support vector regression. The effectiveness of these models is evaluated against self exciting threshold autoregressive model. [ABSTRACT FROM AUTHOR]

The art of logistics distribution involves various stages from the time of supply until the finished product reaches its final consumer [1]. This part of the supply chain process projects, executes and controls circulation, information and storage of the goods and services efficiently and effectively, with the firm purpose of satisfying the needs and requirements of the client [2]. This article begins with a timeline of logistics distribution evolution and changes. Then, the processes that influence the distribution of goods are described in broad strokes, mainly the transport in their different modalities and the costs derived from storage, based on the literature, it ends with a discussion about the added value of logistics in Colombia. [ABSTRACT FROM AUTHOR]

We consider third-order likelihood inferences for the parameters, quantiles and reliability function of the logistic distribution. This theory involves the conditioning and marginalization of the likelihood function. The logistic distribution is a symmetric distribution which is closely related to normal distributions, and which has several applications because of its mathematical tractability and the availability of a closed-form cumulative distribution function. The performance of the third-order techniques is investigated and compared with the first-order techniques using simulations. The results show that the third-order techniques are far more accurate than the usual first-order inference procedures. This results in more accurate inferences about the functions of the parameters of the distribution, which leads to more precise conclusions about the phenomenon modeled by the logistic distribution. [ABSTRACT FROM AUTHOR]

Consider the nonparametric curve estimation problem. Wavelet shrinkage methods are applied to the data in the wavelet domain for noise reduction. After denoising, the function can be estimated by wavelet basis expansion. The present paper proposes a Bayesian approach for wavelet shrinkage with the use of a mixture of a point mass function at zero and the logistic distribution symmetric around zero as the prior distribution to the wavelet coefficients of an unknown function in models with additive Gaussian errors. Statistical properties such as bias, classical and Bayesian risks of the rules are analyzed and performances of the proposed rules are obtained in simulations studies involving the Donoho-Johnstone test functions. Application in a mass spectrometry real data set is done. [ABSTRACT FROM AUTHOR]

This paper addresses the optimal stochastic allocation of distributed energy resources in distribution networks. Typically, uncertain problems are analyzed in multistage formulations, including case generation routines, resulting in computationally exhaustive programs. In this article, two probabilistic approaches are proposed–range probability optimization (RPO) and value probability optimization (VPO)–resulting in a single-stage, convex, stochastic optimal power flow problem. RPO maximizes probabilities within a range of uncertainty, whilst VPO optimizes the values of random variables and maximizes their probabilities. Random variables were modeled with hourly measurements fitted to the logistic distribution. These formulations were tested on two systems and compared against the deterministic case built from expected values. The results indicate that assuming deterministic conditions ends in highly underestimated losses. RPO showed that by including ±10% uncertainty, losses can be increased up to 40% with up to −72% photovoltaic capacity, depending on the system, whereas VPO resulted in up to 85% increases in power losses despite PV installations, with 20% greater probabilities on average. By implementing any of the proposed approaches, it was possible to obtain more probable upper envelopes in the objective, avoiding case generation stages and heuristic methods.

We introduce a new broad and flexible class of multivariate elliptically symmetric distributions including the elliptically symmetric logistic and multivariate normal. Various probabilistic properties of the new distribution are studied, including the distribution of linear transformations, marginal distributions, conditional distributions, moments, stochastic representations and characteristic function. We also consider estimation issues associated with the mean vector and the dispersion matrix. An analysis of a real life data set is presented for illustrative purposes. [ABSTRACT FROM AUTHOR]

In this paper, we introduce bimodal extensions, one symmetric and one asymmetric, of the logistic distribution. We define this new density and study some basic properties. We draw inferences from the moment estimator and maximum likelihood approaches. We present a simulation study to assess the behaviour of the moment and maximum likelihood estimators. We also study the singularity of the Fisher information matrix for particular cases. We offer applications in real data and compare them with a mixture of logistics distributions. [ABSTRACT FROM AUTHOR]

The logistic distribution has been widely used to model growth curves in survival analysis and biological studies. In this article, we propose a goodness of fit test for the logistic distribution based on a new estimate of Kullback-Leibler information. The properties of the test statistic are presented. In order to compute the proposed test statistic, parameters of the logistic distribution are estimated by approximate maximum likelihood estimators (AMLEs) suggested by Balakrishnan and Cohen (1990), which are simple explicit estimators. Through a simulation study, power values of the proposed test are compared with some prominent existing tests. Finally, an illustrative example is presented and analyzed. [ABSTRACT FROM AUTHOR]

We consider log-growth rates of Romanian cities' populations for all cities in the country in the period 1992-2019 on an annual basis. We construct annual, quinquennial and decennial log-growth rates and fit to them thirty-one different statistical distributions. The best results with Kolmogorov–Smirnov, Cramér–von Mises and Anderson–Darling statistics are obtained by a mixture of five stretched Gaussian distributions (5sG) with some fixed parameters, and with the AIC, BIC, HQC information criteria are obtained with mixtures of three logistic distributions (3L), that may have or may have not exponential tails. Just as an illustration, we propose a generating stochastic mechanism for the 3L. Dedicated to Laura Andrés Alcalde [ABSTRACT FROM AUTHOR]

This study addresses the open vehicle routing problem with split deliveries, a variant of the classical vehicle routing problem that allows open routes and partitioned deliveries for customers (i.e., multiple vehicles may serve one customer). This approach may be beneficial for companies interested in reducing their logistics and distribution costs. This study is motivated by a company in the pharmaceutical industry, that seeks to explore the possibility of splitting their deliveries to improve quality indicators related to on-time deliveries and customer satisfaction. Two mixed-integer formulations of the problem are proposed. Additionally, a cutting-plane method is designed to improve the optimization performance. Computational experiments were conducted to validate the performance of the formulations. The second formulation effectiveness was confirmed by providing optimal solutions for instances of up to 30 nodes in a reasonable computational time. The incorporation of the cutting-plane method improves performance with a substantial reduction in the GAP. In the case study, this new approach shows its effectiveness in economic terms by providing savings of up to 20% of the current distribution costs. [ABSTRACT FROM AUTHOR]