New One-Parameter Over-Dispersed Discrete Distribution and Its Application to the Nonnegative Integer-Valued Autoregressive Model of Order One

Irshad, Muhammed Rasheed; Aswathy, Sreedeviamma; Maya, Radhakumari; Nadarajah, Saralees

doi:10.3390/math12010081

Cited by 3 publications

(1 citation statement)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Utilizing big data analytics, advanced statistical algorithms, and data visualization techniques enable the use of sensor data collected from machinery to predict potential faults and implement corresponding maintenance measures. In this field, time series analysis [10][11][12] and anomaly detection [13][14][15][16] have garnered significant attention. Compared to structural models, time series models have more advantages in this aspect as both modeling and forecasting can be readily accomplished.…”

Section: Introductionmentioning

confidence: 99%

Sparsity-Constrained Vector Autoregressive Moving Average Models for Anomaly Detection of Complex Systems with Multisensory Signals

Ma,

Zhang,

Zhai

et al. 2024

Mathematics

View full text Add to dashboard Cite

Detecting anomalies in large, complex systems is a critical and challenging task, and this is especially true for high-dimensional anomaly detection due to the underlying dependency structures among sensors. To incorporate the interrelationships among various sensors, a novel sparsity-constrained vector autoregressive moving average (scVARMA) model is proposed for anomaly detection in complex systems with multisensory signals. This model aims to leverage the inherent relationships and dynamics among various sensor readings, providing a more comprehensive and accurate analysis suitable for complex systems’ complex behavior. This research uses convex optimization to search for a parameterization that is sparse based on the principal of parsimony. This sparse model will not only contribute to meeting the real-time requirements of online monitoring strategies but also keeps the correlations among different sensory signals. The performance of the proposed scVARMA model is validated using real-world data from complex systems. The results affirm the superiority of the proposed scheme, demonstrating its enhanced performance and potential in practical applications.

show abstract

Section: Introductionmentioning

confidence: 99%

Sparsity-Constrained Vector Autoregressive Moving Average Models for Anomaly Detection of Complex Systems with Multisensory Signals

Ma,

Zhang,

Zhai

et al. 2024

Mathematics

View full text Add to dashboard Cite

show abstract

Intrinsic Functional Partially Linear Poisson Regression Model for Count Data

Xu,

Lu,

et al. 2024

Axioms

View full text Add to dashboard Cite

Poisson regression is a statistical method specifically designed for analyzing count data. Considering the case where the functional and vector-valued covariates exhibit a linear relationship with the log-transformed Poisson mean, while the covariates in complex domains act as nonlinear random effects, an intrinsic functional partially linear Poisson regression model is proposed. This model flexibly integrates predictors from different spaces, including functional covariates, vector-valued covariates, and other non-Euclidean covariates taking values in complex domains. A truncation scheme is applied to approximate the functional covariates, and the random effects related to non-Euclidean covariates are modeled based on the reproducing kernel method. A quasi-Newton iterative algorithm is employed to optimize the parameters of the proposed model. Furthermore, to capture the intrinsic geometric structure of the covariates in complex domains, the heat kernel is employed as the kernel function, estimated via Brownian motion simulations. Both simulation studies and real data analysis demonstrate that the proposed method offers significant advantages over the classical Poisson regression model.

show abstract

Analysis of Probability Distributions for Modelling Extreme Rainfall Events and Detecting Climate Change: Insights from Mathematical and Statistical Methods

Montes-Pajuelo,

Rodríguez-Pérez,

López

et al. 2024

Mathematics

View full text Add to dashboard Cite

Exploring the realm of extreme weather events is indispensable for various engineering disciplines and plays a pivotal role in understanding climate change phenomena. In this study, we examine the ability of 10 probability distribution functions—including exponential, normal, two- and three-parameter log-normal, gamma, Gumbel, log-Gumbel, Pearson type III, log-Pearson type III, and SQRT-ET max distributions—to assess annual maximum 24 h rainfall series obtained over a long period (1972–2022) from three nearby meteorological stations. Goodness-of-fit analyses including Kolmogorov–Smirnov and chi-square tests reveal the inadequacy of exponential and normal distributions in capturing the complexity of the data sets. Subsequent frequency analysis and multi-criteria assessment enable us to discern optimal functions for various scenarios, including hydraulic engineering and sediment yield estimation. Notably, the log-Gumbel and three-parameter log-normal distributions exhibit superior performance for high return periods, while the Gumbel and three-parameter log-normal distributions excel for lower return periods. However, caution is advised regarding the overuse of log-Gumbel, due to its high sensitivity. Moreover, as our study considers the application of mathematical and statistical methods for the detection of extreme events, it also provides insights into climate change indicators, highlighting trends in the probability distribution of annual maximum 24 h rainfall. As a novelty in the field of functional analysis, the log-Gumbel distribution with a finite sample size is utilised for the assessment of extreme events, for which no previous work seems to have been conducted. These findings offer critical perspectives on extreme rainfall modelling and the impacts of climate change, enabling informed decision making for sustainable development and resilience.

show abstract

New One-Parameter Over-Dispersed Discrete Distribution and Its Application to the Nonnegative Integer-Valued Autoregressive Model of Order One

Cited by 3 publications

References 26 publications

Sparsity-Constrained Vector Autoregressive Moving Average Models for Anomaly Detection of Complex Systems with Multisensory Signals

Sparsity-Constrained Vector Autoregressive Moving Average Models for Anomaly Detection of Complex Systems with Multisensory Signals

Intrinsic Functional Partially Linear Poisson Regression Model for Count Data

Analysis of Probability Distributions for Modelling Extreme Rainfall Events and Detecting Climate Change: Insights from Mathematical and Statistical Methods

Contact Info

Product

Resources

About