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Principal component analysis (PCA) is a linear dimensionality reduction technique with applications in exploratory data analysis, visualization and data preprocessing.. The data is linearly transformed onto a new coordinate system such that the directions (principal components) capturing the largest variation in the data can be easily identified.
The calculus of variations began with the work of Isaac Newton, such as with Newton's minimal resistance problem, which he formulated and solved in 1685, and later published in his Principia in 1687, [2] which was the first problem in the field to be formulated and correctly solved, [2] and was also one of the most difficult problems tackled by variational methods prior to the twentieth century.
Graph of a linear function Graph of a polynomial function, here a quadratic function. Graph of two trigonometric functions: sine and cosine. A real function is a real-valued function of a real variable, that is, a function whose codomain is the field of real numbers and whose domain is a set of real numbers that contains an interval.
The moment generating function of a real random variable is the expected value of , as a function of the real parameter . For a normal distribution with density f {\displaystyle f} , mean μ {\displaystyle \mu } and variance σ 2 {\textstyle \sigma ^{2}} , the moment generating function exists and is equal to
If X is a random variable taking values in the d-dimensional Euclidean space, X has finite expectation, X ' is an independent identically distributed copy of X, and ‖ ‖ denotes the norm in the Euclidean space, then a simple measure of asymmetry with respect to location parameter θ is ():= ‖ ′ ‖ ‖ + ′ ‖ (=) and dSkew ...
Welch showed that the first confidence procedure dominates the second, according to desiderata from confidence interval theory; for every , the probability that the first procedure contains is less than or equal to the probability that the second procedure contains . The average width of the intervals from the first procedure is less than that ...
R is a programming language for statistical computing and data visualization.It has been adopted in the fields of data mining, bioinformatics and data analysis. [9]The core R language is augmented by a large number of extension packages, containing reusable code, documentation, and sample data.