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Statistical Mechanics : Encyclopedia of Physical Science and Technology, Third Edition, Volume 15. Academic Press. ISBN 978-0-12-227410-7. Bowley, Roger and Sanchez, Mariana (2000). Introductory Statistical Mechanics. Oxford University Press. ISBN 978-0-19-850576-1. {}: CS1 maint: multiple names: authors list [80]
In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. Sometimes called statistical physics or statistical thermodynamics, its applications include many problems in the fields of physics, biology, [1] chemistry, neuroscience, [2] computer science, [3] [4] information theory [5] and ...
The Irwin–Hall distribution is the distribution of the sum of n independent random variables, each of which having the uniform distribution on [0,1]. The Bates distribution is the distribution of the mean of n independent random variables, each of which having the uniform distribution on [0,1]. The logit-normal distribution on (0,1).
In statistics, a unit is one member of a set of entities being studied. It is the main source for the mathematical abstraction of a "random variable".Common examples of a unit would be a single person, animal, plant, manufactured item, or country that belongs to a larger collection of such entities being studied.
Computational statistics, or statistical computing, is the study which is the intersection of statistics and computer science, and refers to the statistical methods that are enabled by using computational methods. It is the area of computational science (or scientific computing) specific to the mathematical science of statistics. This area is ...
Methods of probability theory also apply to descriptions of complex systems given only partial knowledge of their state, as in statistical mechanics or sequential estimation. A great discovery of twentieth-century physics was the probabilistic nature of physical phenomena at atomic scales, described in quantum mechanics .
In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data.This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable.
Estimation theory is a branch of statistics that deals with estimating the values of parameters based on measured empirical data that has a random component. The parameters describe an underlying physical setting in such a way that their value affects the distribution of the measured data.