scholarly journals Log-Transform Kernel Density Estimation of Income Distribution

2016 ◽  
Vol 91 (1-2) ◽  
pp. 141-159 ◽  
Author(s):  
Arthur Charpentier ◽  
Emmanuel Flachaire
Keyword(s):  
Income Distribution ◽  
Density Estimation ◽  
Kernel Density Estimation ◽  
Kernel Density ◽  
Estimation Methods ◽  
Density Functions ◽  
Income Distributions ◽  
Heavy Tailed Distributions ◽  
Heavy Tailed ◽  
Positive Support

Standard kernel density estimation methods are very often used in practice to estimate density functions. It works well in numerous cases. However, it is known not to work so well with skewed, multimodal and heavy-tailed distributions. Such features are usual with income distributions, defined over the positive support. In this paper, we show that a preliminary logarithmic transformation of the data, combined with standard kernel density estimation methods, can provide a much better fit of the density estimation.

scholarly journals Kernel density estimation for heavy-tailed distributions using the champernowne transformation

Statistics ◽  
2005 ◽  
Vol 39 (6) ◽  
pp. 503-516 ◽  
Author(s):  
Tine Buch-larsen ◽  
Jens Perch Nielsen ◽  
Montserrat Guillén ◽  
Catalina Bolancé
Keyword(s):  
Density Estimation ◽  
Kernel Density Estimation ◽  
Kernel Density ◽  
Heavy Tailed Distributions ◽  
Heavy Tailed

scholarly journals Application of Kernel Density Estimation in Lamb Wave-Based Damage Detection

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
Long Yu ◽  
Zhongqing Su
Keyword(s):  
Damage Detection ◽  
Density Estimation ◽  
Kernel Density Estimation ◽  
Lamb Wave ◽  
Kernel Density ◽  
Nonparametric Methods ◽  
Measured Data ◽  
Consensus Algorithm ◽  
Estimation Methods ◽  
Empirical Methods

The present work concerns the estimation of the probability density function (p.d.f.) of measured data in the Lamb wave-based damage detection. Although there was a number of research work which focused on the consensus algorithm of combining all the results of individual sensors, the p.d.f. of measured data, which was the fundamental part of the probability-based method, was still given by experience in existing work. Based on the analysis about the noise-induced errors in measured data, it was learned that the type of distribution was related with the level of noise. In the case of weak noise, the p.d.f. of measured data could be considered as the normal distribution. The empirical methods could give satisfied estimating results. However, in the case of strong noise, the p.d.f. was complex and did not belong to any type of common distribution function. Nonparametric methods, therefore, were needed. As the most popular nonparametric method, kernel density estimation was introduced. In order to demonstrate the performance of the kernel density estimation methods, a numerical model was built to generate the signals of Lamb waves. Three levels of white Gaussian noise were intentionally added into the simulated signals. The estimation results showed that the nonparametric methods outperformed the empirical methods in terms of accuracy.

scholarly journals Moment-Based Density Approximation Techniques as Applied to Heavy-tailed Distributions

2019 ◽  
Vol 8 (3) ◽  
pp. 1
Author(s):  
John Sang Jin Kang ◽  
Serge B. Provost ◽  
Jiandong Ren
Keyword(s):  
Density Estimation ◽  
Density Functions ◽  
Density Approximation ◽  
Simulation Studies ◽  
Esscher Transform ◽  
Approximation Techniques ◽  
Heavy Tailed Distributions ◽  
Heavy Tailed ◽  
Made In

Several advances are made in connection with the approximation and estimation of heavy-tailed distributions. It is first explained that on initially applying the Esscher transform to heavy-tailed density functions such as the Pareto, Studentt and Cauchy, said densities can be approximated by employing a certain moment-based methodology. Alternatively, density approximants can be obtained by appropriately truncating such distributions or mapping them onto finite supports. These techniques are then extended to the context of density estimation, their validity being demonstrated by means of simulation studies. As well, illustrative actuarial examples are presented.

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