# Beta Distribution - Statistics

I am not sure if the process that I am currently using is statistically correct. I have some data that are arranged with a beta distribution. I need to generate randomly another set of data with the same statistic distribution. Firstly, I 'elaborate' the original data by dividing each number $$n$$ for the sum of all the data $$\sum{n}$$. Then I proceed to obtain the average $$\mu$$ and the standard deviation $$\sigma$$. Then I proceed to obtain the shape factors $$\alpha$$ and $$\beta$$. To do this, I use the following formulas: $$\alpha = (\frac{1-\mu}{\sigma^2} - (\frac{1}{\mu}))\mu^2$$, and $$\beta = \alpha (\frac{1}{\mu} - 1)$$. Once I obtain this values I use the function from Excel $$BETA.INV(RAND(), \alpha, \beta)$$. This returns me a value between 0 and 1. How do I go from this number to the respective number just like the one of the original set? Do I multiply this number for the $$\sum{}n$$.

• You seem to be using the method of moments to estimate the parameters $\alpha$ and $\beta.$ The maximum likelihood estimates (shown later in the same Wikipedia article) are better. // You seem to be generating only one observation from the beta distribution once you estimated the parameters. (You can get more observations by generating more uniform random variables within your Excel formula. – BruceET Nov 29 '18 at 16:56