Functions, Processes & Transforms

  Characteristic Function- Inverse of Fourier transform of CF is PDF:

Moment-generating function- Measures of central tendency and dispersion. Points represent probability density, then the 0^th moment = total probability (i.e. one), 1^st = µ, 2^nd = s², 3^rd = skewness and 4^th = kurtosis.

Laplace Transform- converts integral and differential equations into algebraic equations. From the time domain to the frequency domain. Expresses a function as a superposition of moments