# Maximum likelihood estimator

1. Feb 22, 2005

### semidevil

Maximum likelihood estimator....

ok, i'm stil a bit lost...so tell me if this is right:

$$f_y(y;\theta) = \frac{2y}{\theta^2}, for 0 < y < \theta$$

find the MLE estimator for theta.

$$L(\theta) = 2yn\theta^{-2 \sum_1^n y_i$$.

is this even right to begin with?

then take the natural log

$$ln2yn + -2\sum_1^n y_i * ln\theta$$

take derivative

$$\frac {1}{2yn} -\frac{ 2 * \sum_1^n yi}{\theta}.$$

now how do I solve this in terms of theta? and after that, what do I do next?

this just doesnt look right

and I also need to find it using the method of moments, but I get $$\frac {y^4}{2\theta}$$ after the integral...

and this one too...this looks too messy:

$$fy(y;\theta) = \frac{y^3e^{\frac{-y}{\theta}}}{6\theta^4}$$

Last edited: Feb 22, 2005