scholarly journals A Bimodal Extension of the Exponential Distribution with Applications in Risk Theory

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 679
Author(s):  
Jimmy Reyes ◽  
Emilio Gómez-Déniz ◽  
Héctor W. Gómez ◽  
Enrique Calderín-Ojeda
Keyword(s):  
Exponential Distribution ◽  
Hazard Rate ◽  
Rate Function ◽  
Estimation Methods ◽  
Inverse Gaussian ◽  
New Family ◽  
Tail Distribution ◽  
Zero Values ◽  
The Mean ◽  
Positive Support

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.

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

2018 ◽  
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.

A novel heavy tail distribution of logarithmic returns of cryptocurrencies

2021 ◽  
pp. 102574
Author(s):  
Quang Van Tran ◽  
Jaromir Kukal
Keyword(s):  
Heavy Tail ◽  
Tail Distribution

scholarly journals Design and Pricing of Chinese Contingent Convertible Bonds

2014 ◽  
Vol 2 (5) ◽  
pp. 428-436 ◽  
Author(s):  
Ping Li ◽  
Jie Liu
Keyword(s):  
Stock Return ◽  
Banking System ◽  
Convertible Bonds ◽  
Stochastic Volatility Model ◽  
Too Big To Fail ◽  
Regulatory Requirements ◽  
Significant Cost ◽  
Contingent Capital ◽  
Tail Distribution ◽  
Volatility Model

AbstractThe financial crisis since 2007 has highlighted the fragility of the banking system. To address this deficiency, the Basel committee has agreed upon Basel III which consists of reinforcing banks’ capital through new regulatory requirements. Raising additional funds by issuing common equity would lead to a significant cost for banks. Facing the problem, regulators came up with the concept of contingent capital. Contingent convertible (Coco) bonds have been the topic as both a solution to the “too big to fail” problem and a measure by which financial institutions can save themselves. In this paper we first give the introduction of Coco bonds, then present the design of Chinese Coco bonds and pricing Coco bonds through an equity derivative approach as well as sensitivity analysis based on B-S-M hypothesis. Considering that the stock return follows fat-tail distribution, this paper uses Heston stochastic volatility model to price Coco bonds. Finally we give some proposals for developing Coco bonds market in China.

scholarly journals Fluctuations of company yearly profits vs. scaled revenue: Fat-tail distribution of Lévy type

2008 ◽  
Vol 84 (6) ◽  
pp. 68003 ◽  
Author(s):  
H. E. Roman ◽  
R. A. Siliprandi ◽  
Ch. Dose ◽  
C. Riccardi ◽  
M. Porto
Keyword(s):  
Fat Tail ◽  
Tail Distribution
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