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Showing posts with label quotient. Show all posts
Showing posts with label quotient. Show all posts

26 September, 2021

RAND() function: Distribution of the ratios of TWO Rand() functions

Excel Rand() function generates a random real number in a standard continuous  UNIFORM distribution of less than 1 and equal/greater than 0. It means that in this distribution every value between 0 and 1 is equally likely to be chosen.The mean of the distribution is 0.5. The variance is equal to 1/12 (=0.083333).

The Rand() function is used mainly as a random number generator. It's distribution is pretty simple and straightforward. Much more interesting are distributions of quotient (ratio), product, difference or sum of two independently run Rand() functions. Their usefulness in practical applications is not yet well defined.

I've looked closer at the distribution function of the quotient, denoted here as F(z), where z=X2/X1. The result of distribution, based on the sample of 2000 outcomes (vertical axis) is presented on the following chart (z on horizontal axis):