22 papers · ranked by Valyu relevance
Asghar Ghasemi, Saleh Zahediasl
Statistical errors are common in scientific literature and about 50% of the published articles have at least one error. The assumption of normality needs to be checked for many statistical procedures, namely parametric tests, because their validity depends on it. The aim of this commentary is to overview checking for…
M. M. Hammad
Statistics provides us with the means to make sense of data, uncover patterns, and draw meaningful conclusions from seemingly complex information. It has applications in a wide range of disciplines, including science, engineering, finance, social sciences, and many others. Meanwhile, Mathematica, a powerful…
Steven A. Frank
Size varies. Small things are typically more frequent than large things. The logarithm of frequency often declines linearly with the logarithm of size. That power law relation forms one of the common patterns of nature. Why does the complexity of nature reduce to such a simple pattern? Why do things as different as…
Kai-Tai Fang, Yu-Xuan Lin, Yu-Hui Deng, Nikolai Leonenko + 1 more
Statistical modeling is fundamentally based on probability distributions, which can be discrete or continuous and univariate or multivariate. This review focuses on the methods used to construct these distributions, covering both traditional and newly developed approaches. We first examine classic distributions such as…
Abhranil Das, Wilson S. Geisler
Univariate and multivariate normal probability distributions are widely used when modeling decisions under uncertainty. Computing the performance of such models requires integrating these distributions over specific domains, which can vary widely across models. Besides some special cases where these integrals are easy…
Steven A. Frank
Size varies. Small things are typically more frequent than large things. The logarithm of frequency often declines linearly with the logarithm of size. That power law relation forms one of the common patterns of nature. Why does the complexity of nature reduce to such a simple pattern? Why do things as different as…
Ronald F. Fox, Theodore P. Hill
In every finite mixture of different normal distributions, there will always be exactly one of those distributions that not only is over-represented in the right tail of the mixture, but even completely overwhelms all other subpopulations in the rightmost tails. This property, although not unique to normal…
Omar Eidous, Mohammad Al-Rawash
In this paper, we introduce a new approximation of the cumulative distribution function of the standard normal distribution based on Tocher's approximation. Also, we assess the quality of the new approximation using two criteria namely the maximum absolute error and the mean absolute error. The approximation is…
Alex Capaldi, Tiffany N. Kolba, Eugene Demidenko
We propose novel estimators for the parameters of an exponential distribution and a normal distribution when the only known information is a sample of sample maxima; i.e., the known information consists of a sample of m values, each of which is the maximum of a sample of n independent random variables drawn from the…
Laurence de Torrenté, Samuel Zimmerman, Masako Suzuki, Maximilian Christopeit + 2 more
In genomics, we often impose the assumption that gene expression data follows a specific distribution. However, rarely do we stop to question this assumption or consider its applicability to all genes in the transcriptome. Our study investigated the prevalence of genes with expression distributions that are non-Normal…
Sharon Lee, Geoffrey J. McLachlan
Parametric distributions are an important part of statistics. There is now a voluminous literature on different fascinating formulations of flexible distributions. We present a selective and brief overview of a small subset of these distributions, focusing on those that are obtained by scaling the mean and/or…
Philip D. Gingerich
The zero-force evolutionary law (ZFEL) of McShea et al. states that independently evolving entities, with no forces or constraints acting on them, will tend to accumulate differences and therefore diverge from each other. McShea et al. quantified the law by assuming normality on an additive arithmetic scale and…
Tadamasa Sawada
Consider randomly sampling variables from an infinite population[fn0001] and computing their normalized-sum, which is the difference between the average of the variables and the mean of the population multiplied by the square-root of the sample size. The Central-limit Theorem (CLT) assures us that this normalized-sum…
Evan M. Koch
Neutral models for quantitative trait evolution are useful for identifying phenotypes under selection in natural populations. Models of quantitative traits often assume phenotypes are normally distributed. This assumption may be violated when a trait is affected by relatively few genetic variants or when the effects of…
Gauss M. Cordeiro, Renato J. Cintra, Leandro Chaves Rêgo, Edwin M. M. Ortega
'Edwin M. M. Ortega'] A five-parameter distribution called the McDonald normal distribution is defined and studied. The new distribution contains, as special cases, several important distributions discussed in the literature, such as the normal, skew-normal, exponentiated normal, beta normal and Kumaraswamy normal…
Nahla Ben Salah
The q-Gaussian is a probability distribution generalizing the Gaussian one. In spite of a q-normal distribution is popular, there is a problem when calculating an expectation value with a corresponding normalized distribution and not a q-normal distribution itself. In this paper, two q-moments types called normalized…
Shunzhou Wan, Agastya Bhati, David Wright, Ian Wall + 3 more
Optimization of binding affinities for ligands to their target protein is a primary objective in rational drug discovery. Herein we report on a collaborative study that evaluates various compounds designed to bind to the SET and MYND domain-containing protein 3 (SMYD3). SMYD3 is a histone methyltransferase and plays an…
Martin Robinson, Alan Bond, Alexandr Simonov, Jie Zhang + 1 more
Recently, we have introduced the use of techniques drawn from Bayesian statistics to recover kinetic and thermodynamic parameters from voltammetric data, and were able to show that the technique of large amplitude ac voltammetry yielded significantly more accurate parameter values than the equivalent dc approach. In…
Sterling Baird, Jason R. Hall, Taylor D. Sparks
Would you rather search for a line inside a cube or a point inside a square? Physics-based simulations and wet-lab experiments often have symmetries (degeneracies) that allow reducing problem dimensionality or search space, but constraining these degeneracies is often unsupported or difficult to implement in many…
Paul Morris, Cory Simon
In many gas sensing tasks, we simply wish to become aware of gas compositions that deviate from normal, "business-as-usual" conditions. We provide a methodology, illustrated by example, to computationally predict the performance of a gas sensor array design for detecting anomalous gas compositions. Specifically, we…
Guillaume A. Rousselet, Rand R. Wilcox
To summarise skewed (asymmetric) distributions, such as reaction times, typically the mean or the median are used as measures of central tendency. Using the mean might seem surprising, given that it provides a poor measure of central tendency for skewed distributions, whereas the median provides a better indication of…
Steven A. Frank, Jordi Bascompte
The abundance of different species in a community often follows the log series distribution. Other ecological patterns also have simple forms. Why does the complexity and variability of ecological systems reduce to such simplicity? Common answers include maximum entropy, neutrality, and convergent outcome from…