I have to estimate ( using method of moments) $\theta$ with an estimator $\hat{\theta}$ for a function with pdf given as $$\theta x^{\theta-1}, \ \ \ \text{ for 0 < x < 1, and } 0 \ \text{ otherwise}$$.

I found that that the $\hat{\theta} = \frac{\bar{x}}{1-\bar{x}}$, but now I need to estimate the $\theta$ in program R.

So, first I define $\theta$ as follows: $$\hat{\theta} = function(sample) \{ rbeta(n = 100, shape1 = \theta, shape2 = 1 \}$$

Here I am already stuck, because I don't know the value of $\theta$? Maybe there is some known value used for parameter $\alpha$ in Beta distribution?


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