Related papers: Transformation of arbitrary distributions to the n…
Transforming a random variable to improve its normality leads to a followup test for whether the transformed variable follows a normal distribution. Previous work has shown that the Anderson Darling test for normality suffers from…
Box-Cox power transformation is a commonly used methodology to transform the distribution of a non-normal data into a normal one. Estimation of the transformation parameter is crucial in this methodology. In this study, the estimation…
Many real data sets contain numerical features (variables) whose distribution is far from normal (gaussian). Instead, their distribution is often skewed. In order to handle such data it is customary to preprocess the variables to make them…
Covariate adjustment is an important tool in the analysis of randomized clinical trials and observational studies. It can be used to increase efficiency and thus power, and to reduce possible bias. While most statistical tests in randomized…
The log-transform is a common tool in statistical analysis, reducing the impact of extreme values, compressing the range of reported values for improved visualization, enabling the usage of parametric statistical tests requiring normally…
The Cox model is an indispensable tool for time-to-event analysis, particularly in biomedical research. However, medicine is undergoing a profound transformation, generating data at an unprecedented scale, which opens new frontiers to study…
Studies of the effects of medical interventions increasingly take place in distributed research settings using data from multiple clinical data sources including electronic health records and administrative claims. In such settings, privacy…
Meta-analysis is the aggregation of data from multiple studies to find patterns across a broad range relating to a particular subject. It is becoming increasingly useful to apply meta-analysis to summarize these studies being done across…
Modern data analysis frequently involves variables with highly non-Gaussian marginal distributions. However, commonly used analysis methods are most effective with roughly Gaussian data. This paper introduces an automatic transformation…
Forecasts of statistical constraints on model parameters using the Fisher matrix abound in many fields of astrophysics. The Fisher matrix formalism involves the assumption of Gaussianity in parameter space and hence fails to predict complex…
Logarithmic transformation of the data has been recommended by the literature in the case of highly skewed distributions such as those commonly found in information science. The purpose of the transformation is to make the data conform to…
The mainstream theory of hypothesis testing in high-dimensional regression typically assumes the underlying true model is a low-dimensional linear regression model, yet the Box-Cox transformation is a regression technique commonly used to…
We revisit the replica method for analyzing inference and learning in parametric models, considering situations where the data-generating distribution is unknown or analytically intractable. Instead of assuming idealized distributions to…
Testing the equality of two proportions is a common procedure in science, especially in medicine and public health. In these domains it is crucial to be able to quantify evidence for the absence of a treatment effect. Bayesian hypothesis…
The Box-Cox transformation is applied to the linear mixed models for analyzing positive and grouped data. The problem in using Box Cox transformation is that the maximum likelihood estimator of the transformation parameter is generally…
We present a method to transform multivariate unimodal non-Gaussian posterior probability densities into approximately Gaussian ones via non-linear mappings, such as Box--Cox transformations and generalisations thereof. This permits an…
The log-normal distribution is used to describe the positive data, that it has skewed distribution with small mean and large variance. This distribution has application in many sciences for example medicine, economics, biology and…
The problem of transformation selection is thoroughly treated from a Bayesian perspective. Several families of transformations are considered with a view to achieving normality: the Box-Cox, the Modulus, the Yeo & Johnson and the Dual…
Recently, several studies proposed non-linear transformations, such as a logarithmic or Gaussianization transformation, as efficient tools to recapture information about the (Gaussian) initial conditions. During non-linear evolution, part…
The central limit theorem ensures that a sum of random variables tends to a Gaussian distribution as their total number tends to infinity. However, for a class of positive random variables, we find that the sum tends faster to a log-normal…