momentskvörðanum

Momentskvörðanum is a term of Icelandic origin that can be roughly translated to "moment quotient" or "ratio of moments." In a statistical context, it refers to a method for estimating parameters of a probability distribution by equating sample moments to theoretical moments. This technique is a foundational concept in statistical inference and was notably developed by Karl Pearson.

The core idea behind momentskvörðanum is that the statistical moments of a sample (such as the mean, variance, skewness, and kurtosis) should approximate the corresponding theoretical moments of the underlying probability distribution from which the sample was drawn. By setting up equations where the calculated sample moments are equal to the formulas for the theoretical moments, one can then solve these equations to find estimates for the unknown parameters of the distribution. For example, to estimate the mean and variance of a normal distribution, one would equate the sample mean to the theoretical mean (μ) and the sample variance to the theoretical variance (σ²).

While momentskvörðanum is conceptually straightforward and often provides good initial estimates, it can sometimes be less efficient than other estimation methods like maximum likelihood estimation, especially for smaller sample sizes or more complex distributions. However, its simplicity and intuitive appeal have made it a valuable tool in statistical analysis, particularly for introducing the principles of parameter estimation. The method is widely taught in introductory statistics courses.