Quantum Gravity 404.4: The Logistic Distribution is Fat-Tailed (Relates to Logistic Differential Equation)
in [Physics]
|
Prev: JSH: Prime Gap proven and approved byLSU by muslims pure Maths Teachers
Next: *****Re: EARTH'S CHANGING MAGNETIC POLES
From: Osher Doctorow on 28 Jul 2010 03:58 From Osher Doctorow It turns out that the Logistic probability distribution is also fat- tailed or heavy-tailed, which is important for Probable Causation/ Influence (PI) since the Riccati Differential Equation and its Logistic Differential Equation and Exponential Growth/Decay subtypes are important in PI. See Wikipedia's online "Kurtosis", "Logistic Distribution", "t Distribution" or "Student's t distribution", etc. The Gaussian/ Normal distribution has 0 excess kurtosis (a measure of fat-tailed and peakedness at least for symmetric distributions), while the Logistic Distribution has excess kurtosis 6/5 and the t-distribution has excess kurtosis 6/(k - 4) for k > 4. It is difficult to compare these with the exponential distribution because the latter is nonnegative asymmetric while the others are both negative and positive on the whole real line and are symmetric, and the excess kurtosis of the exponential distribution is enormously distorted compared to the others because of this (it is 6). The logistic probability distribution is just the logistic differential equation except that the derivative is replaced by the defining symbol of the logistic probability density function in the former. Osher Doctorow
From: Osher Doctorow on 28 Jul 2010 04:14
From Osher Doctorow Recall that the logistic differential equation: 1) dy/dt = ky(1 - y) for y normalized into [0, 1] (that is, y a variable in [0, 1]), k real constant (often taken > 0) is an expansion-contraction equation in the sense that y (for example, population percent of a particular group or category) tends to grow or expand/increase, while 1 - y represents its tendency to contract or decrease due to such things as environmental constraints (inability of the environment to support a population as it gets too larger, etc.). It can be solved by separation of variables and partial fraction decomposition of y(1 - y) and turns out to be a ratio of (linear functions) of exponentials or negative exponentials in time. Osher Doctorow |