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32 pages, 907 KiB  
Article
A New Exponentiated Power Distribution for Modeling Censored Data with Applications to Clinical and Reliability Studies
by Kenechukwu F. Aforka, H. E. Semary, Sidney I. Onyeagu, Harrison O. Etaga, Okechukwu J. Obulezi and A. S. Al-Moisheer
Symmetry 2025, 17(7), 1153; https://doi.org/10.3390/sym17071153 - 18 Jul 2025
Viewed by 914
Abstract
This paper presents the exponentiated power shanker (EPS) distribution, a fresh three-parameter extension of the standard Shanker distribution with the ability to extend a wider class of data behaviors, from right-skewed and heavy-tailed phenomena. The structural properties of the distribution, namely complete and [...] Read more.
This paper presents the exponentiated power shanker (EPS) distribution, a fresh three-parameter extension of the standard Shanker distribution with the ability to extend a wider class of data behaviors, from right-skewed and heavy-tailed phenomena. The structural properties of the distribution, namely complete and incomplete moments, entropy, and the moment generating function, are derived and examined in a formal manner. Maximum likelihood estimation (MLE) techniques are used for estimation of parameters, as well as a Monte Carlo simulation study to account for estimator performance across varying sample sizes and parameter values. The EPS model is also generalized to a regression paradigm to include covariate data, whose estimation is also conducted via MLE. Practical utility and flexibility of the EPS distribution are demonstrated through two real examples: one for the duration of repairs and another for HIV/AIDS mortality in Germany. Comparisons with some of the existing distributions, i.e., power Zeghdoudi, power Ishita, power Prakaamy, and logistic-Weibull, are made through some of the goodness-of-fit statistics such as log-likelihood, AIC, BIC, and the Kolmogorov–Smirnov statistic. Graphical plots, including PP plots, QQ plots, TTT plots, and empirical CDFs, further confirm the high modeling capacity of the EPS distribution. Results confirm the high goodness-of-fit and flexibility of the EPS model, making it a very good tool for reliability and biomedical modeling. Full article
(This article belongs to the Section Mathematics)
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29 pages, 7122 KiB  
Article
Experimental Study on Two Types of Novel Prefabricated Counterfort Retaining Wall: Performance Characteristics and Earth Pressure Reduction Effect of Geogrids
by Ao Luo, Yutao Feng, Detan Liu, Junjie Wang, Shi Wang, Huikun Ling and Shiyuan Huang
Coatings 2025, 15(7), 841; https://doi.org/10.3390/coatings15070841 - 18 Jul 2025
Viewed by 309
Abstract
Conventional cast-in-place counterfort retaining walls, while widely used to support the fill body in geotechnical engineering cases, suffer from extended construction cycles and environmental impacts that constrain their usage more widely. In this study, in order to overcome these limitations, the performance of [...] Read more.
Conventional cast-in-place counterfort retaining walls, while widely used to support the fill body in geotechnical engineering cases, suffer from extended construction cycles and environmental impacts that constrain their usage more widely. In this study, in order to overcome these limitations, the performance of two types of innovative prefabricated counterfort retaining wall system—a monolithic design and a modular design—was investigated through physical modeling. The results reveal that failure mechanisms are fundamentally governed by the distribution of stress at the connection interfaces. The monolithic system, with fewer connections, concentrates stress and is more vulnerable to cracking at the primary joints. In contrast, the modular system disperses loads across numerous connections, reducing localized stress. Critically, this analysis identified a construction-dependent failure mode: incomplete contact between the foundation and the base slab induces severe bending moments that can lead to catastrophic failure. Furthermore, this study shows that complex stress states due to backfill failure can induce detrimental tensile forces on the wall structure. To address this, a composite soil material–wall structure system incorporating geogrid reinforcement was developed. This system significantly enhances the backfill’s bearing capacity and mitigates adverse loading. Based on the comprehensive analysis of settlement and structural performance, the optimal configuration involves concentrating geogrid layers in the upper third of section of the backfill, with sparser distribution below. Full article
(This article belongs to the Special Issue Novel Cleaner Materials for Pavements)
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26 pages, 2873 KiB  
Article
Interactive Content Retrieval in Egocentric Videos Based on Vague Semantic Queries
by Linda Ablaoui, Wilson Estecio Marcilio-Jr, Lai Xing Ng, Christophe Jouffrais and Christophe Hurter
Multimodal Technol. Interact. 2025, 9(7), 66; https://doi.org/10.3390/mti9070066 - 30 Jun 2025
Viewed by 612
Abstract
Retrieving specific, often instantaneous, content from hours-long egocentric video footage based on hazily remembered details is challenging. Vision–language models (VLMs) have been employed to enable zero-shot textual-based content retrieval from videos. But, they fall short if the textual query contains ambiguous terms or [...] Read more.
Retrieving specific, often instantaneous, content from hours-long egocentric video footage based on hazily remembered details is challenging. Vision–language models (VLMs) have been employed to enable zero-shot textual-based content retrieval from videos. But, they fall short if the textual query contains ambiguous terms or users fail to specify their queries enough, leading to vague semantic queries. Such queries can refer to several different video moments, not all of which can be relevant, making pinpointing content harder. We investigate the requirements for an egocentric video content retrieval framework that helps users handle vague queries. First, we narrow down vague query formulation factors and limit them to ambiguity and incompleteness. Second, we propose a zero-shot, user-centered video content retrieval framework that leverages a VLM to provide video data and query representations that users can incrementally combine to refine queries. Third, we compare our proposed framework to a baseline video player and analyze user strategies for answering vague video content retrieval scenarios in an experimental study. We report that both frameworks perform similarly, users favor our proposed framework, and, as far as navigation strategies go, users value classic interactions when initiating their search and rely on the abstract semantic video representation to refine their resulting moments. Full article
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19 pages, 660 KiB  
Article
A Versatile Distribution Based on the Incomplete Gamma Function: Characterization and Applications
by Jimmy Reyes, Carolina Marchant, Karol I. Santoro and Yuri A. Iriarte
Mathematics 2025, 13(11), 1749; https://doi.org/10.3390/math13111749 - 25 May 2025
Viewed by 498
Abstract
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 [...] Read more.
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 article belongs to the Section D1: Probability and Statistics)
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32 pages, 626 KiB  
Review
Integrating Energy Storage Technologies with Renewable Energy Sources: A Pathway Toward Sustainable Power Grids
by Farhan H. Malik, Ghulam A. Hussain, Yahia M. S. Alsmadi, Zunaib M. Haider, Wathiq Mansoor and Matti Lehtonen
Sustainability 2025, 17(9), 4097; https://doi.org/10.3390/su17094097 - 1 May 2025
Cited by 1 | Viewed by 2140
Abstract
The fact that electricity needs to be consumed at the same moment it is generated makes it very complicated to match supply and demand at all times. With the evolution of more and more intermittent renewable energy sources in the system, it has [...] Read more.
The fact that electricity needs to be consumed at the same moment it is generated makes it very complicated to match supply and demand at all times. With the evolution of more and more intermittent renewable energy sources in the system, it has become more challenging to meet demand and supply in real time, hence the demand for energy storage systems to optimize energy costs and ease grid operations. The need for these systems arises because of the intermittency and uncontrollable production of wind, solar, and tidal energy sources. Therefore, a storage system that can store energy produced from renewable energy sources and then convert it into electrical energy when required is highly needed. Modern energy storage technologies play a pivotal role in the storage of energy produced through unconventional methods. This review paper discusses technical details and features of various types of energy storage systems and their capabilities of integration into the power grid. An analysis of various energy storage systems being utilized in the power grid is also presented. A review of a technology would be incomplete without the study of its ramifications for the environment. Therefore, the effect of various energy storage technologies on the environment is also a part of this comprehensive study. Full article
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30 pages, 3076 KiB  
Article
Constant Stress-Partially Accelerated Life Tests of Vtub-Shaped Lifetime Distribution under Progressive Type II Censoring
by Aisha Fayomi, Asmaa A. Ahmed, Neama T. AL-Sayed, Sara M. Behairy, Asmaa M. Abd AL-Fattah, Gannat R. AL-Dayian and Abeer A. EL-Helbawy
Symmetry 2024, 16(9), 1251; https://doi.org/10.3390/sym16091251 - 23 Sep 2024
Viewed by 1202
Abstract
In lifetime tests, the waiting time for items to fail may be long under usual use conditions, particularly when the products have high reliability. To reduce the cost of testing without sacrificing the quality of the data obtained, the products are exposed to [...] Read more.
In lifetime tests, the waiting time for items to fail may be long under usual use conditions, particularly when the products have high reliability. To reduce the cost of testing without sacrificing the quality of the data obtained, the products are exposed to higher stress levels than normal, which quickly causes early failures. Therefore, accelerated life testing is essential since it saves costs and time. This paper considers constant stress-partially accelerated life tests under progressive Type II censored samples. This is realized under the claim that the lifetime of products under usual use conditions follows Vtub-shaped lifetime distribution, which is also known as log-log distribution. The log–log distribution is highly significant and has several real-world applications since it has distinct shapes of its probability density function and hazard rate function. A graphical description of the log–log distribution is exhibited, including plots of the probability density function and hazard rate. The log–log density has different shapes, such as decreasing, unimodal, and approximately symmetric. Several mathematical properties, such as quantiles, probability weighted moments, incomplete moments, moments of residual life, and reversed residual life functions, and entropy of the log–log distribution, are discussed. In addition, the maximum likelihood and maximum product spacing methods are used to obtain the interval and point estimators of the acceleration factor, as well as the model parameters. A simulation study is employed to assess the implementation of the estimation approaches under censoring schemes and different sample sizes. Finally, to demonstrate the viability of the various approaches, two real data sets are investigated. Full article
(This article belongs to the Section Mathematics)
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18 pages, 9732 KiB  
Article
Hyperpolarized 13C NMR Reveals Pathway Regulation in Lactococcus lactis and Metabolic Similarities and Differences Across the Tree of Life
by Sebastian Meier, Alexandra L. N. Zahid, Lucas Rebien Jørgensen, Ke-Chuan Wang, Peter Ruhdal Jensen and Pernille Rose Jensen
Molecules 2024, 29(17), 4133; https://doi.org/10.3390/molecules29174133 - 30 Aug 2024
Cited by 2 | Viewed by 1557
Abstract
The control of metabolic networks is incompletely understood, even for glycolysis in highly studied model organisms. Direct real-time observations of metabolic pathways can be achieved in cellular systems with 13C NMR using dissolution Dynamic Nuclear Polarization (dDNP NMR). The method relies on [...] Read more.
The control of metabolic networks is incompletely understood, even for glycolysis in highly studied model organisms. Direct real-time observations of metabolic pathways can be achieved in cellular systems with 13C NMR using dissolution Dynamic Nuclear Polarization (dDNP NMR). The method relies on a short-lived boost of NMR sensitivity using a redistribution of nuclear spin states to increase the alignment of the magnetic moments by more than four orders of magnitude. This temporary boost in sensitivity allows detection of metabolism with sub-second time resolution. Here, we hypothesized that dDNP NMR would be able to investigate molecular phenotypes that are not easily accessible with more conventional methods. The use of dDNP NMR allows real-time insight into carbohydrate metabolism in a Gram-positive bacterium (Lactoccocus lactis), and comparison to other bacterial, yeast and mammalian cells shows differences in the kinetic barriers of glycolysis across the kingdoms of life. Nevertheless, the accumulation of non-toxic precursors for biomass at kinetic barriers is found to be shared across the kingdoms of life. We further find that the visualization of glycolysis using dDNP NMR reveals kinetic characteristics in transgenic strains that are not evident when monitoring the overall glycolytic rate only. Finally, dDNP NMR reveals that resting Lactococcus lactis cells use the influx of carbohydrate substrate to produce acetoin rather than lactate during the start of glycolysis. This metabolic regime can be emulated using suitably designed substrate mixtures to enhance the formation of the C4 product acetoin more than 400-fold. Overall, we find that dDNP NMR provides analytical capabilities that may help to clarify the intertwined mechanistic determinants of metabolism and the optimal usage of biotechnologically important bacteria. Full article
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18 pages, 4135 KiB  
Article
Effective Temporal Graph Learning via Personalized PageRank
by Ziyu Liao, Tao Liu, Yue He and Longlong Lin
Entropy 2024, 26(7), 588; https://doi.org/10.3390/e26070588 - 10 Jul 2024
Cited by 2 | Viewed by 2012
Abstract
Graph representation learning aims to map nodes or edges within a graph using low-dimensional vectors, while preserving as much topological information as possible. During past decades, numerous algorithms for graph representation learning have emerged. Among them, proximity matrix representation methods have been shown [...] Read more.
Graph representation learning aims to map nodes or edges within a graph using low-dimensional vectors, while preserving as much topological information as possible. During past decades, numerous algorithms for graph representation learning have emerged. Among them, proximity matrix representation methods have been shown to exhibit excellent performance in experiments and scale to large graphs with millions of nodes. However, with the rapid development of the Internet, information interactions are happening at the scale of billions every moment. Most methods for similarity matrix factorization still focus on static graphs, leading to incomplete similarity descriptions and low embedding quality. To enhance the embedding quality of temporal graph learning, we propose a temporal graph representation learning model based on the matrix factorization of Time-constrained Personalize PageRank (TPPR) matrices. TPPR, an extension of personalized PageRank (PPR) that incorporates temporal information, better captures node similarities in temporal graphs. Based on this, we use Single Value Decomposition or Nonnegative Matrix Factorization to decompose TPPR matrices to obtain embedding vectors for each node. Through experiments on tasks such as link prediction, node classification, and node clustering across multiple temporal graphs, as well as a comparison with various experimental methods, we find that graph representation learning algorithms based on TPPR matrix factorization achieve overall outstanding scores on multiple temporal datasets, highlighting their effectiveness. Full article
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23 pages, 308 KiB  
Concept Paper
Social Theory and Navigating Indeterminacy: A Configurational Analysis of Iranian Youth’s Identity Construction in Contemporary Iran
by Abbas Jong
Societies 2024, 14(3), 32; https://doi.org/10.3390/soc14030032 - 21 Feb 2024
Cited by 3 | Viewed by 3792
Abstract
An emerging disparity within contemporary social science highlights a disconnection between the world in the process of metamorphosing and cosmopolitanization and the knowledge of the social world that is still trapped in the cognitive assumptions of modern episteme, which provided the conditions for [...] Read more.
An emerging disparity within contemporary social science highlights a disconnection between the world in the process of metamorphosing and cosmopolitanization and the knowledge of the social world that is still trapped in the cognitive assumptions of modern episteme, which provided the conditions for the emergence of modern social sciences a century ago. This divide inhibits the efficacy of social analysis in comprehending and elucidating contemporary phenomena. This article advocates for a shift in the ontology of social theory and science towards the cosmopolitanization of the world, characterized by the prioritization of indeterminacy and fluidity in the construction of social phenomena. It investigates the epistemological implications and prerequisites of this ontological transformation, favoring a post-foundationalist approach as the most suitable epistemological framework. In response to the challenges posed by the uncertainty and indeterminacy of cosmopolitanization, after reviewing some of the existing theoretical efforts to address and provide alternatives to this challenge, the article proposes the examination of social configurations as the most fitting subjects for study. This approach necessitates the suspension of conventional, given, regulated categories, and trans-historical theories. It underscores the importance of recognizing configurations as incomplete, contingent units shaped within specific historical contexts and moments. The fluidity, relationality, and indeterminacy of configurations situated between the universal and the singular make them suitable for analysis at the level of particular. After elaborating on the most important features of social configurations, finally, by employing the proposed theoretical framework, this article aims to investigate its effectiveness in analyzing the process of identity construction among Iranian youth in Tehran in the context of the cosmopolitanization of reality, particularly in the face of the Islamist regime of Iran’s official politics of identity. Through a review and revision of selected empirical studies on youth identity construction in the consumer spaces of Tehran, based on the idea of social configurations within the framework of cosmopolitanization, it is argued that the genuine understanding of identity politics in contemporary Iran is not rooted in conventional analytical norms and categories but rather in a comprehensible conceptual apparatus characterized by fluidity and indeterminacy, capable of effectively making sense of the conflict between the politics of determinacy and indeterminacy in Iranian everyday life. Full article
(This article belongs to the Special Issue Young People’s Constructions of Identities: Global Perspectives)
18 pages, 6649 KiB  
Article
Geometry of Enumerable Class of Surfaces Associated with Mylar Balloons
by Vladimir I. Pulov, Vasyl Kovalchuk and Ivaïlo M. Mladenov
Mathematics 2024, 12(4), 557; https://doi.org/10.3390/math12040557 - 12 Feb 2024
Viewed by 1158
Abstract
In this paper, the very fundamental geometrical characteristics of the Mylar balloon like the profile curve, height, volume, arclength, surface area, crimping factor, etc. are recognized as geometrical moments In(x) and In and this observation has been used [...] Read more.
In this paper, the very fundamental geometrical characteristics of the Mylar balloon like the profile curve, height, volume, arclength, surface area, crimping factor, etc. are recognized as geometrical moments In(x) and In and this observation has been used to introduce an infinite family of surfaces Sn specified by the natural numbers n=0,1,2,. These surfaces are presented via explicit formulas (through the incomplete Euler’s beta function) and can be identified as an interesting family of balloons. Their parameterizations is achieved relying on the well-known relationships among elliptic integrals, beta and gamma functions. The final results are expressed via the fundamental mathematical constants, such as π and the lemniscate constant ϖ. Quite interesting formulas for recursive calculations of various quantities related to associated figures modulo four are derived. The most principal results are summarized in a table, illustrated via a few graphics, and some direct relationships with other fundamental areas in mathematics, physics, and geometry are pointed out. Full article
(This article belongs to the Section B: Geometry and Topology)
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31 pages, 2699 KiB  
Article
Engineering Applications with Stress-Strength for a New Flexible Extension of Inverse Lomax Model: Bayesian and Non-Bayesian Inference
by Salem A. Alyami, I. Elbatal, Amal S. Hassan and Ehab M. Almetwally
Axioms 2023, 12(12), 1097; https://doi.org/10.3390/axioms12121097 - 29 Nov 2023
Cited by 5 | Viewed by 1436
Abstract
In this paper, we suggest a brand new extension of the inverse Lomax distribution for fitting engineering time data. The newly developed distribution, termed the transmuted Topp–Leone inverse Lomax (TTLILo) distribution, is characterized by an additional shape and transmuted parameters. It is critical [...] Read more.
In this paper, we suggest a brand new extension of the inverse Lomax distribution for fitting engineering time data. The newly developed distribution, termed the transmuted Topp–Leone inverse Lomax (TTLILo) distribution, is characterized by an additional shape and transmuted parameters. It is critical to notice that the skewness, kurtosis, and tail weights of the distribution are strongly influenced by these additional characteristics of the extra parameters. The TTLILo model is capable of producing right-skewed, J-shaped, uni-modal, and reversed-J-shaped densities. The proposed model’s statistical characteristics, including the moments, entropy values, stochastic ordering, stress-strength model, incomplete moments, and quantile function, are examined. Moreover, characterization based on two truncated moments is offered. Using Bayesian and non-Bayesian estimating techniques, we estimate the distribution parameters of the suggested distribution. The bootstrap procedure, approximation, and Bayesian credibility are the three forms of confidence intervals that have been created. A simulation study is used to assess the efficiency of the estimated parameters. The TTLILo model is then put to the test by being applied to actual engineering datasets, demonstrating that it offers a good match when compared to alternative models. Two applications based on real engineering datasets are taken into consideration: one on the failure times of airplane air conditioning systems and the other on the active repair times of airborne communication transceivers. Also, we consider the problem of estimating the stress-strength parameter R=P(Z2<Z1) with engineering application. Full article
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11 pages, 790 KiB  
Article
Patient-Related Factors Associated with Adverse Outcomes Following Weaning from Veno-Arterial Extracorporeal Membrane Oxygenation
by Marius Keller, Henning Gloeckner, Sibel Sari-Yavuz, Helene A. Haeberle, Christian Schlensak, Peter Rosenberger, Harry Magunia and Michael Koeppen
J. Clin. Med. 2023, 12(23), 7406; https://doi.org/10.3390/jcm12237406 - 29 Nov 2023
Viewed by 1266
Abstract
Background: Veno-arterial extracorporeal membrane oxygenation (vaECMO) removal reflects a critical moment and factors of adverse outcomes are incompletely understood. Thus, we studied various patient-related factors during vaECMO removal to determine their association with outcomes. Methods: A total of 58 patients from a university [...] Read more.
Background: Veno-arterial extracorporeal membrane oxygenation (vaECMO) removal reflects a critical moment and factors of adverse outcomes are incompletely understood. Thus, we studied various patient-related factors during vaECMO removal to determine their association with outcomes. Methods: A total of 58 patients from a university hospital were included retrospectively. Demographic, clinical, and echocardiographic parameters were recorded while under vaECMO support, as well as the need for inotropic and vasoactive-inotropic scores (VIS). Successful weaning was defined as 28-day survival without reinitiation of vaECMO. Results: Patient age differed significantly between patients with a successful and a failed vaECMO weaning (54 ± 14 vs. 62 ± 12 years, p = 0.029). In univariable logistic regression, age (OR 0.952 (0.909–0.997), p = 0.038), the necessities for inotropic agents at the time of echocardiography (OR 0.333 (0.113–0.981), p = 0.046), and vaECMO removal (OR 0.266 (0.081–0.877), p = 0.030) as well as the dobutamine dose during removal (OR 0.649 (0.473–0.890), p = 0.007), were significantly associated with a successful weaning from vaECMO. Age (HR 1.048 (1.006–1.091), p = 0.024) and the VIS (HR 1.030 (1.004–1.056), p = 0.025) at the time of vaECMO removal were independently associated with survival in bivariable Cox regression. In Kaplan–Meier analysis, a VIS of >5.1 at vaECMO removal was associated with impaired survival (log-rank p = 0.025). Conclusions: In this cohort, age and the extent of vasoactive-inotropic agents were associated with adverse outcomes following vaECMO, whereas echocardiographic biventricular function during vaECMO support was not. Full article
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20 pages, 936 KiB  
Article
The Logistic Burr XII Distribution: Properties and Applications to Income Data
by Renata Rojas Guerra, Fernando A. Peña-Ramírez and Gauss M. Cordeiro
Stats 2023, 6(4), 1260-1279; https://doi.org/10.3390/stats6040078 - 21 Nov 2023
Cited by 3 | Viewed by 2376
Abstract
We define and study the four-parameter logistic Burr XII distribution. It is obtained by inserting the three-parameter Burr XII distribution as the baseline in the logistic-X family and may be a useful alternative method to model income distribution and could be applied to [...] Read more.
We define and study the four-parameter logistic Burr XII distribution. It is obtained by inserting the three-parameter Burr XII distribution as the baseline in the logistic-X family and may be a useful alternative method to model income distribution and could be applied to other areas. We illustrate that the new distribution can have decreasing and upside-down-bathtub hazard functions and that its density function is an infinite linear combination of Burr XII densities. Some mathematical properties of the proposed model are determined, such as the quantile function, ordinary and incomplete moments, and generating function. We also obtain the maximum likelihood estimators of the model parameters and perform a Monte Carlo simulation study. Further, we present a parametric regression model based on the introduced distribution as an alternative to the location-scale regression model. The potentiality of the new distribution is illustrated by means of two applications to income data sets. Full article
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14 pages, 522 KiB  
Article
Slash-Weighted Lindley Distribution: Properties, Inference, and Applications
by Jaime S. Castillo, Inmaculada Barranco-Chamorro, Osvaldo Venegas and Héctor W. Gómez
Mathematics 2023, 11(18), 3980; https://doi.org/10.3390/math11183980 - 19 Sep 2023
Cited by 2 | Viewed by 1243
Abstract
The slash-weighted Lindley model is introduced due to the need to obtain a model with more kurtosis than the weighted Lindley distribution. Several expressions for the pdf of this model are given. Its cumulative distribution function is expressed in terms of a generalized [...] Read more.
The slash-weighted Lindley model is introduced due to the need to obtain a model with more kurtosis than the weighted Lindley distribution. Several expressions for the pdf of this model are given. Its cumulative distribution function is expressed in terms of a generalized hypergeometric function and the incomplete gamma function. Moments and maximum likelihood estimation were studied. A simulation study was carried out to illustrate the good performance of the estimates. Finally, two real applications are included. Full article
(This article belongs to the Section D1: Probability and Statistics)
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19 pages, 3359 KiB  
Article
Asymmetric Right-Skewed Size-Biased Bilal Distribution with Mathematical Properties, Reliability Analysis, Inference and Applications
by Amer Ibrahim Al-Omari, Rehab Alsultan and Ghadah Alomani
Symmetry 2023, 15(8), 1578; https://doi.org/10.3390/sym15081578 - 13 Aug 2023
Cited by 2 | Viewed by 1418
Abstract
Asymmetric distributions, as opposed to symmetric distributions, may be more resilient to extreme values or outliers. Furthermore, when data show substantial skewness, asymmetric distributions can shed light on the underlying processes or phenomena being investigated. In this direction, the size-biased Bilal distribution (SBBD) [...] Read more.
Asymmetric distributions, as opposed to symmetric distributions, may be more resilient to extreme values or outliers. Furthermore, when data show substantial skewness, asymmetric distributions can shed light on the underlying processes or phenomena being investigated. In this direction, the size-biased Bilal distribution (SBBD) is suggested in this study as a generalization to the Bilal distribution. The length-biased and area-biased Bilal distributions are discussed in detail as two special cases. The main statistical properties of the distribution including the rth moment, coefficients of variation, skewness, kurtosis, moment generating function, incomplete moments, moments of residual life, harmonic mean, Fisher’s information, and the Rényi entropy as a measure of uncertainty are presented. Graphical representations of the cumulative distribution, probability density, odds, survival, hazard, reversed hazard rate, and cumulative hazard functions are presented for further explanation of the distribution behavior. In addition, the methods of moments and maximum likelihood estimates are taken into account for estimating the model parameters. A simulation study is carried out to see the efficiency of the maximum likelihood in terms of standard errors and bias. Real data sets of precipitation and myeloid leukemia patients are considered to show the practical significance of the suggested distributions as an alternative to some well-known distributions such as the Rama, Rani, Bilal, and exponential distributions. It is found that the size-biased Bilal distribution is right-skewed and has a superior fitting performance compared to the other distributions in this study. Full article
(This article belongs to the Special Issue Symmetry in Probability Theory and Statistics)
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