The h-Core and h-Tail Distribution with Dynamic Metrics

There are some generalizations of the classical exponential distribution in the statistical literature that have proven to be helpful in numerous scenarios. Some of these distributions are the families of distributions that were proposed by Marshall and Olkin and Gupta. The disadvantage of these models is the impossibility of fitting data of a bimodal nature of incorporating covariates in the model in a simple way. Some empirical datasets with positive support, such as losses in insurance portfolios, show an excess of zero values and bimodality. For these cases, classical distributions, such as exponential, gamma, Weibull, or inverse Gaussian, to name a few, are unable to explain data of this nature. This paper attempts to fill this gap in the literature by introducing a family of distributions that can be unimodal or bimodal and nests the exponential distribution. Some of its more relevant properties, including moments, kurtosis, Fisher’s asymmetric coefficient, and several estimation methods, are illustrated. Different results that are related to finance and insurance, such as hazard rate function, limited expected value, and the integrated tail distribution, among other measures, are derived. Because of the simplicity of the mean of this distribution, a regression model is also derived. Finally, examples that are based on actuarial data are used to compare this new family with the exponential distribution.

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Safety-First Portfolio Linear Program Using Sampled Tail Distribution

2008 4th International Conference on Wireless Communications, Networking and Mobile Computing ◽

10.1109/wicom.2008.2301 ◽

2008 ◽

Author(s):

Kuo-Hwa Chang ◽

Yu-Lin Chiang ◽

Yang-Shu Lu

Keyword(s):

Linear Program ◽

Tail Distribution ◽

Safety First

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Dynamic Daylight Metrics for Electricity Savings in Offices: Window Size and Climate Smart Lighting Management

Energies ◽

10.3390/en11113143 ◽

2018 ◽

Vol 11 (11) ◽

pp. 3143 ◽

Cited By ~ 6

Author(s):

Ignacio Acosta ◽

Miguel Ángel Campano ◽

Samuel Domínguez-Amarillo ◽

Carmen Muñoz

Keyword(s):

Energy Efficiency ◽

Net Present Value ◽

Energy Savings ◽

Performance Metrics ◽

Control Strategies ◽

Window Size ◽

Weather Conditions ◽

Worst Case ◽

Daylight Performance ◽

Dynamic Metrics

Daylight performance metrics provide a promising approach for the design and optimization of lighting strategies in buildings and their management. Smart controls for electric lighting can reduce power consumption and promote visual comfort using different control strategies, based on affordable technologies and low building impact. The aim of this research is to assess the energy efficiency of these smart controls by means of dynamic daylight performance metrics, to determine suitable solutions based on the geometry of the architecture and the weather conditions. The analysis considers different room dimensions, with variable window size and two mean surface reflectance values. DaySim 3.1 lighting software provides the simulations for the study, determining the necessary quantification of dynamic metrics to evaluate the usefulness of the proposed smart controls and their impact on energy efficiency. The validation of dynamic metrics is carried out by monitoring a mesh of illuminance-meters in test cells throughout one year. The results showed that, for most rooms more than 3.00 m deep, smart controls achieve worthwhile energy savings and a low payback period, regardless of weather conditions and for worst-case situations. It is also concluded that dimming systems provide a higher net present value and allow the use of smaller window size than other control solutions.

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Tail Distribution Function

Encyclopedia of Operations Research and Management Science ◽

10.1007/978-1-4419-1153-7_200841 ◽

2013 ◽

pp. 1544-1544

Keyword(s):

Distribution Function ◽

Tail Distribution

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Does Tail Label Help for Large-Scale Multi-Label Learning

Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2018/395 ◽

2018 ◽

Cited By ~ 5

Author(s):

Tong Wei ◽

Yu-Feng Li

Keyword(s):

Large Scale ◽

Performance Metrics ◽

Learning Algorithm ◽

Predictive Performance ◽

Low Complexity ◽

Tail Distribution ◽

Prediction Time ◽

Unseen Data ◽

Model Size ◽

Fast Prediction

Large-scale multi-label learning annotates relevant labels for unseen data from a huge number of candidate labels. It is well known that in large-scale multi-label learning, labels exhibit a long tail distribution in which a significant fraction of labels are tail labels. Nonetheless, how tail labels make impact on the performance metrics in large-scale multi-label learning was not explicitly quantified. In this paper, we disclose that whatever labels are randomly missing or misclassified, tail labels impact much less than common labels in terms of commonly used performance metrics (Top-$k$ precision and nDCG@$k$). With the observation above, we develop a low-complexity large-scale multi-label learning algorithm with the goal of facilitating fast prediction and compact models by trimming tail labels adaptively. Experiments clearly verify that both the prediction time and the model size are significantly reduced without sacrificing much predictive performance for state-of-the-art approaches.

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