Category Archives: Calculus

Cumulants and the Cornish-Fisher Expansion

“Consider the following.” (Bill Nye the Science Guy) There are random variables drawn from the same kind of probability distribution, but with different parameters for each. In this example, I’ll consider random variables , that is, each drawn from a … Continue reading

Posted in Calculus, closed-form expressions, Cornish-Fisher expansion, cumulants, descriptive statistics, mathematics, maths, multivariate statistics, statistical models, statistics, theoretical statistics | Leave a comment

When linear systems can’t be solved by linear means

Linear systems of equations and their solution form the cornerstone of much Engineering and Science. Linear algebra is a paragon of Mathematics in the sense that its theory is what mathematicians try to emulate when they develop theory for many … Continue reading

Posted in Calculus, dynamic linear models, mathematics, maths, nloptr, numerical algorithms, numerical analysis, numerical linear algebra, numerics, SVD | Leave a comment

Merry Newtonmas tomorrow! On finding the area of the Batman Shape using Monte Carlo integration

It’s Newtonmas 2017 tomorrow! What better way to celebrate than talk about integration! The Batman Shape (sometimes called the Batman Curve, somewhat erroneously, I think) looks like this: You can find details about it at Wolfram MathWorld, including its area … Continue reading

Posted in Bayes, Calculus, Markov Chain Monte Carlo | Tagged , , , , | 1 Comment