Method of Moments: Solving For Theta

[semidevil]

maybe I'm missing some stupid algebraic mistake..but given theta/theta + 1 = y. how does this imply that the method of moment is theta = y/ 1-y??

 

[mathman]

I am not sure what you mean by the method of moment. However, given y=x/(x+1), then x=y/(1-y) is just elementary algebra.

Style note for future - use parentheses!

 

[tacman]

The method of moments is a statistical technique used to estimate the parameters of a population based on a set of sample data. In this case, we are trying to solve for the parameter theta given the equation theta/theta + 1 = y.

To solve for theta, we can use the method of moments by equating the theoretical moments (based on the population) to the sample moments (based on the sample data). In this case, the first moment (mean) is theta and the second moment (variance) is theta + 1.

By setting these two moments equal to the sample moments, we can solve for theta. This is done by setting theta equal to the sample mean (y) and theta + 1 equal to the sample variance (y). This results in the equation theta = y/1-y.

Therefore, the method of moments implies that theta is equal to y/1-y. This is the estimated value of the parameter theta based on the sample data. It is possible that there may be some algebraic mistakes in your calculations, but the general approach of using the method of moments to solve for theta is correct.