[Read more...]

The Kruskal-Wallis test extends the Mann-Whitney-Wilcoxon Rank Sum test for more than two groups. The test is nonparametric similar to the Mann-Whitney test and as such does not assume the data are normally distributed and can, therefore, be used when the assumption of normality is violated. This example will employ ... [Read more...]

[Read more...]

Part 2 of 2 in the series Random Number GenerationMultiplicative congruential generators, also known as Lehmer random number generators, is a type of linear congruential generator for generating pseudorandom numbers in . The multiplicative congruential generator, often abbreviated as MLCG or MCG, is defined as a recurrence relation similar to... The post Multiplicative ... [Read more...]

Part of 1 in the series Random Number GenerationA Linear congruential generator (LCG) is a class of pseudorandom number generator (PRNG) algorithms used for generating sequences of random-like numbers. The generation of random numbers plays a large role in many applications ranging from cryptography to Monte Carlo methods. Linear congruential... The ... [Read more...]

[Read more...]

[Read more...]

[Read more...]

[Read more...]

Part 1 of 5 in the series Numerical AnalysisNeville’s method evaluates a polynomial that passes through a given set of and points for a particular value using the Newton polynomial form. Neville’s method is similar to a now-defunct procedure named Aitken’s algorithm and is based on the divided differences ... [Read more...]

[Read more...]

Part 5 of 5 in the series Set TheoryOrdered and Unordered Pairs A pair set is a set with two members, for example, , which can also be thought of as an unordered pair, in that . However, we seek a more a strict and rich object that tells us... The post Set Theory ... [Read more...]

[Read more...]

Part 3 of 3 in the series Set TheoryThe union and intersection set operations were introduced in a previous post using two sets, and . These set operations can be generalized to accept any number of sets. Arbitrary Set Unions Operation Consider a set of infinitely many sets: It would... The post Set ... [Read more...]

[Read more...]

Sets define a ‘collection’ of objects, or things typically referred to as ‘elements’ or ‘members.’ The concept of sets arises naturally when dealing with any collection of objects, whether it be a group of numbers or anything else. Conceptually, the following examples can be defined as a ‘set’: {1, 2,... The post ... [Read more...]

The more common approach to QR decomposition is employing Householder reflections rather than utilizing Gram-Schmidt. In practice, the Gram-Schmidt procedure is not recommended as it can lead to cancellation that causes inaccuracy of the computation of , which may result in a non-orthogonal matrix. Householder reflections are another method of... The ... [Read more...]

QR decomposition is another technique for decomposing a matrix into a form that is easier to work with in further applications. The QR decomposition technique decomposes a square or rectangular matrix, which we will denote as , into two components, , and . Where is an orthogonal matrix, and is... The post QR ... [Read more...]

[Read more...]

The iterated principal factor method is an extension of the principal factor method that seeks improved estimates of the communality. As seen in the previous post on the principal factor method, initial estimates of or are found to obtain from which the factors are computed. In the iterated principal factor... ... [Read more...]