MLEmenetelmän

MLEmenetelmän, often referred to as the Method of Estimating Moments, is a statistical technique used for parameter estimation in probability distributions. It is based on the principle of equating sample moments to the corresponding theoretical moments of a distribution. The theoretical moments are functions of the unknown parameters of the distribution. By calculating the sample moments from observed data and setting them equal to these theoretical moment functions, a system of equations is formed. Solving this system of equations allows for the estimation of the unknown parameters.

The first few moments are commonly used, with the first moment (the mean) and the second moment (related to variance) being the most frequent choices. For example, to estimate the parameters of a normal distribution, the sample mean would be equated to the theoretical mean (which is a parameter, mu), and the sample variance would be equated to the theoretical variance (which is another parameter, sigma squared). This method is generally straightforward to implement, especially for distributions where the theoretical moments are easily expressed in terms of the parameters.

While MLEmenetelmän is intuitive and often provides consistent estimators, it is not always the most efficient method. Maximum Likelihood Estimation (MLE) is a competing method that often yields estimators with smaller variances, especially for large sample sizes. However, MLEmenetelmän can be a useful starting point or a viable alternative when MLE is computationally complex or difficult to derive. Its simplicity makes it applicable in various statistical modeling contexts.