The Lambert Way to Gaussianize Heavy-Tailed Data with the Inverse of Tukey's h Transformation as a Special Case
نویسنده
چکیده
I present a parametric, bijective transformation to generate heavy tail versions of arbitrary random variables. The tail behavior of this heavy tail Lambert W × F X random variable depends on a tail parameter δ ≥ 0: for δ = 0, Y ≡ X, for δ > 0 Y has heavier tails than X. For X being Gaussian it reduces to Tukey's h distribution. The Lambert W function provides an explicit inverse transformation, which can thus remove heavy tails from observed data. It also provides closed-form expressions for the cumulative distribution (cdf) and probability density function (pdf). As a special case, these yield analytic expression for Tukey's h pdf and cdf. Parameters can be estimated by maximum likelihood and applications to S&P 500 log-returns demonstrate the usefulness of the presented methodology. The R package Lambert W implements most of the introduced methodology and is publicly available on CRAN.
منابع مشابه
On Exponential Power Distribution And Poultry Feeds Data: A Case Study
Abstract. In this paper, we propose to study a generalized form of the exponential power distribution which contains others in the literature as special cases. This unifying exponential power distribution is characterized by a parameter ω and a function h(ω) which regulates the tail behavior of the distribution, thus making it more flexible and suitable for modeling than the usual normal di...
متن کاملThe Family of Scale-Mixture of Skew-Normal Distributions and Its Application in Bayesian Nonlinear Regression Models
In previous studies on fitting non-linear regression models with the symmetric structure the normality is usually assumed in the analysis of data. This choice may be inappropriate when the distribution of residual terms is asymmetric. Recently, the family of scale-mixture of skew-normal distributions is the main concern of many researchers. This family includes several skewed and heavy-tailed d...
متن کاملImpact of Hindon River Water on Selected Riparian Flora (Azadirachta Indica and Acacia Nilotica) with special Reference to Heavy Metals
The present study aims to identify the impact of polluted aquatic body i.e. River Hindon on two selected riparian flora i.e. Azadirachta indica and Acacia nilotica. During the course of study the average concentration of different metals in river water was found as Iron (Fe) 11.27ppm±3.50, Manganese (Mn) 4.00ppm±1.26, Cadmium (Cd) 0.08ppm±0.07, Nickel (Ni) 0.63ppm±0.17 and Zinc (Zn) 1.46ppm±0.3...
متن کاملImpact of Hindon River Water on Selected Riparian Flora (Azadirachta Indica and Acacia Nilotica) with special Reference to Heavy Metals
The present study aims to identify the impact of polluted aquatic body i.e. River Hindon on two selected riparian flora i.e. Azadirachta indica and Acacia nilotica. During the course of study the average concentration of different metals in river water was found as Iron (Fe) 11.27ppm±3.50, Manganese (Mn) 4.00ppm±1.26, Cadmium (Cd) 0.08ppm±0.07, Nickel (Ni) 0.63ppm±0.17 and Zinc (Zn) 1.46ppm±0.3...
متن کاملTime Series Modeling of Coronavirus (COVID-19) Spread in Iran
Various types of Coronaviruses are enveloped RNA viruses from the Corona-viridae family and part of the Coronavirinae subfamily. This family of viruses affects neurological, gastrointestinal, hepatic, and respiratory systems. Recently, a new memb-er of this family, named Covid-19, is moving around the world. The expansion of Covid-19 carries many risks, and its control requires strict planning ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
دوره 2015 شماره
صفحات -
تاریخ انتشار 2015