Monday, April 17, 2017

The Trapazoidal Distribution

  Over the weekend I've been studying the Trapazoidal Distribution. One only needs two numbers a and b to define this distribution. Its height, h, can be found since the area under the curve equals 1.

I wrote an Excel user function to generate 1000 random numbers that fit this distribution with a=0.5 and b=1 then determined the observed frequencies for the following set of intervals.

To check the trapazoidal random number generator it was necessary to determine the distribution which best fit the data. To do this a search was necessary to find the values for a and b which minimized the root mean square error for the fit. Since the trapazoidal distribution is symmetric it can be folded horizontally to reduce the number of intervals needed in the calculation.

The fit turned out to be fairly good.

Above the blue dots represent the observed frequencies and the blue line is the fit.

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