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semidevil
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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??
The method of moments is a statistical technique used to estimate the parameters of a probability distribution based on a set of sample data. It involves equating the theoretical moments of the distribution to the sample moments to find the values of the parameters.
The method of moments works by equating the sample moments, such as the mean and variance, to their theoretical counterparts. This creates a system of equations that can be solved to find the values of the parameters of the distribution.
The purpose of using the method of moments is to estimate the parameters of a probability distribution when the underlying distribution is unknown or cannot be easily determined. It is a simple and intuitive method that can provide accurate estimates when certain assumptions are met.
The method of moments relies on the assumptions that the sample data is representative of the underlying population, and that the moments of the distribution can be accurately estimated from the sample moments. It also assumes that the distribution is continuous and has a finite number of parameters.
The method of moments may not provide accurate estimates if the underlying distribution is not well-represented by the sample data, or if the sample size is too small. It also assumes that the distribution is known, which may not always be the case. Additionally, it may not work well for distributions with heavier tails or extreme values.