Adelchi Azzalini (born 1951) is an Italian statistician and educator. He is known for research in likelihood inference and multivariate statistics including the development of skew normal distributions. [1] [2] [3]
Azzalini was born in Milan and received his laurea in statistics and economics from the University of Padua in 1975. He carried out his military service for a year before working as a research assistant at the University of Padua. In 1978, Azzalini moved to the UK and studied at the Imperial College London, where he received his MSc and PhD, both in statistics, in 1979 and 1981, respectively. His PhD supervisor was David Cox. Azzalini returned to Padua to take on a researcher position in 1981 and became a professor at the University of Padua in 1986 and remained there since. [4] [5]
Azzalini is a fellow of the Royal Statistical Society, [4] a member of the Bernoulli Society for Mathematical Statistics and Probability and served as the editor of the Bernoulli News in 2000. [6] In 2011, a workshop was held at the Pontifical Catholic University of Chile to honor Azzalini's contribution to the development of the skew-normal distribution. [7]
Multivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable, i.e., multivariate random variables. Multivariate statistics concerns understanding the different aims and background of each of the different forms of multivariate analysis, and how they relate to each other. The practical application of multivariate statistics to a particular problem may involve several types of univariate and multivariate analyses in order to understand the relationships between variables and their relevance to the problem being studied.
Statistical inference is the process of using data analysis to infer properties of an underlying distribution of probability. Inferential statistical analysis infers properties of a population, for example by testing hypotheses and deriving estimates. It is assumed that the observed data set is sampled from a larger population.
Mathematical statistics is the application of probability theory, a branch of mathematics, to statistics, as opposed to techniques for collecting statistical data. Specific mathematical techniques which are used for this include mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure theory.
This glossary of statistics and probability is a list of definitions of terms and concepts used in the mathematical sciences of statistics and probability, their sub-disciplines, and related fields. For additional related terms, see Glossary of mathematics and Glossary of experimental design.
Ole Eiler Barndorff-Nielsen was a Danish statistician who has contributed to many areas of statistical science.
Kantilal Vardichand "Kanti" Mardia is an Indian-British statistician specialising in directional statistics, multivariate analysis, geostatistics, statistical bioinformatics and statistical shape analysis. He was born in Sirohi, Rajasthan, India in a Jain family and now resides and works in Leeds. He is known for his series of tests of multivariate normality based measures of multivariate skewness and kurtosis as well as work on the statistical measures of shape.
In statistics, normality tests are used to determine if a data set is well-modeled by a normal distribution and to compute how likely it is for a random variable underlying the data set to be normally distributed.
In probability theory and statistics, the skew normal distribution is a continuous probability distribution that generalises the normal distribution to allow for non-zero skewness.
The generalized normal distribution or generalized Gaussian distribution (GGD) is either of two families of parametric continuous probability distributions on the real line. Both families add a shape parameter to the normal distribution. To distinguish the two families, they are referred to below as "symmetric" and "asymmetric"; however, this is not a standard nomenclature.
In statistics, the precision matrix or concentration matrix is the matrix inverse of the covariance matrix or dispersion matrix, . For univariate distributions, the precision matrix degenerates into a scalar precision, defined as the reciprocal of the variance, .
In probability and statistics, an elliptical distribution is any member of a broad family of probability distributions that generalize the multivariate normal distribution. Intuitively, in the simplified two and three dimensional case, the joint distribution forms an ellipse and an ellipsoid, respectively, in iso-density plots.
Gábor J. Székely is a Hungarian-American statistician/mathematician best known for introducing energy statistics (E-statistics). Examples include: the distance correlation, which is a bona fide dependence measure, equals zero exactly when the variables are independent; the distance skewness, which equals zero exactly when the probability distribution is diagonally symmetric; the E-statistic for normality test; and the E-statistic for clustering.
Nancy Margaret Reid is a Canadian theoretical statistician. She is a professor at the University of Toronto where she holds a Canada Research Chair in Statistical Theory. In 2015 Reid became Director of the Canadian Institute for Statistical Sciences.
Fang Kaitai, also known as Kai-Tai Fang, is a Chinese mathematician and statistician who has helped to develop generalized multivariate analysis, which extends classical multivariate analysis beyond the multivariate normal distribution to more general elliptical distributions. He has also contributed to the design of experiments.
Fernando de Helguero was an Italian mathematician, statistician and pioneer of biostatistics.
Likelihoodist statistics or likelihoodism is an approach to statistics that exclusively or primarily uses the likelihood function. Likelihoodist statistics is a more minor school than the main approaches of Bayesian statistics and frequentist statistics, but has some adherents and applications. The central idea of likelihoodism is the likelihood principle: data are interpreted as evidence, and the strength of the evidence is measured by the likelihood function. Beyond this, there are significant differences within likelihood approaches: "orthodox" likelihoodists consider data only as evidence, and do not use it as the basis of statistical inference, while others make inferences based on likelihood, but without using Bayesian inference or frequentist inference. Likelihoodism is thus criticized for either not providing a basis for belief or action, or not satisfying the requirements of these other schools.
In statistics, a sequence of random variables is homoscedastic if all its random variables have the same finite variance; this is also known as homogeneity of variance. The complementary notion is called heteroscedasticity, also known as heterogeneity of variance. The spellings homoskedasticity and heteroskedasticity are also frequently used. Assuming a variable is homoscedastic when in reality it is heteroscedastic results in unbiased but inefficient point estimates and in biased estimates of standard errors, and may result in overestimating the goodness of fit as measured by the Pearson coefficient.
Hannu Frans Vilhelm Oja is a Finnish mathematical statistician and biostatistician known for his contribution to nonparametric inference, robust statistics, and multivariate statistical methods. He introduced the Oja median for multivariate distributions.