Analysis and Presentation of Experimental Results by Costas Christodoulides & George Christodoulides

Author:Costas Christodoulides & George Christodoulides
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

The function of the probability density is normalized. It has a parabolic shape (see figure below) with a minimum equal to 0 at . Due to the symmetry of the distribution, the mean value of x is . This distribution was chosen as an example of an anti-Gaussian distribution since results near the mean have very small probability of being observed, while the opposite happens for values near the edges of the distribution.

The standard deviation of this distribution is

The Monte Carlo method will be used again in the simulation of the measurement procedure. 10 000 random numbers, , between 0 and 1, with 5 significant figures each, were found exactly as in the last example, using the first 50 000 decimal digits of π. The correspondence of these random numbers to values of is a little more difficult than in the last example, because now the values of are not uniformly distributed between 0 and 1. As the way in which this will be achieved is of general importance for the Monte Carlo method, we will describe it in some detail.

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