Search results
Results from the WOW.Com Content Network
Because is a linear differential operator, the solution () to a general system of this type can be written as an integral over a distribution of source given by (): = (, ′) (′) ′ where the Green's function for Laplacian in three variables (, ′) describes the response of the system at the point to a point source located at ...
The Laplace–Stieltjes transform of a real-valued function g is given by a Lebesgue–Stieltjes integral of the form ()for s a complex number.As with the usual Laplace transform, one gets a slightly different transform depending on the domain of integration, and for the integral to be defined, one also needs to require that g be of bounded variation on the region of integration.
In mathematics, the Stieltjes transformation S ρ (z) of a measure of density ρ on a real interval I is the function of the complex variable z defined outside I by the formula S ρ ( z ) = ∫ I ρ ( t ) d t t − z , z ∈ C ∖ I . {\displaystyle S_{\rho }(z)=\int _{I}{\frac {\rho (t)\,dt}{t-z}},\qquad z\in \mathbb {C} \setminus I.}
3.2 Linear transformations. ... Download as PDF; Printable version; ... Compositional data in three variables can be plotted via ternary plots.
For example, suppose that the values x are realizations from different Poisson distributions: i.e. the distributions each have different mean values μ. Then, because for the Poisson distribution the variance is identical to the mean, the variance varies with the mean. However, if the simple variance-stabilizing transformation
A Markov process is called a reversible Markov process or reversible Markov chain if there exists a positive stationary distribution π that satisfies the detailed balance equations [13] =, where P ij is the Markov transition probability from state i to state j, i.e. P ij = P(X t = j | X t − 1 = i), and π i and π j are the equilibrium probabilities of being in states i and j, respectively ...
Variable changes for differentiation and integration are taught in elementary calculus and the steps are rarely carried out in full. The very broad use of variable changes is apparent when considering differential equations, where the independent variables may be changed using the chain rule or the dependent variables are changed resulting in ...
Gaussian processes are useful in statistical modelling, benefiting from properties inherited from the normal distribution. For example, if a random process is modelled as a Gaussian process, the distributions of various derived quantities can be obtained explicitly. Such quantities include the average value of the process over a range of times ...