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In statistics, a generalized estimating equation (GEE) is used to estimate the parameters of a generalized linear model with a possible unmeasured correlation between observations from different timepoints. [1] [2]
The generalized additive model for location, scale and shape (GAMLSS) is a semiparametric regression model in which a parametric statistical distribution is assumed for the response (target) variable but the parameters of this distribution can vary according to explanatory variables.
In statistics, generalized least squares (GLS) is a method used to estimate the unknown parameters in a linear regression model.It is used when there is a non-zero amount of correlation between the residuals in the regression model.
In statistics, a generalized linear model (GLM) is a flexible generalization of ordinary linear regression.The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value.
In econometrics and statistics, the generalized method of moments (GMM) is a generic method for estimating parameters in statistical models.Usually it is applied in the context of semiparametric models, where the parameter of interest is finite-dimensional, whereas the full shape of the data's distribution function may not be known, and therefore maximum likelihood estimation is not applicable.
where is the beta function, is the location parameter, > is the scale parameter, < < is the skewness parameter, and > and > are the parameters that control the kurtosis. and are not parameters, but functions of the other parameters that are used here to scale or shift the distribution appropriately to match the various parameterizations of this distribution.
Then, select from the set of Hill estimators {^} = which are roughly constant with respect to : these stable values are regarded as reasonable estimates for the shape parameter . If X 1 , ⋯ , X n {\displaystyle X_{1},\cdots ,X_{n}} are i.i.d., then the Hill's estimator is a consistent estimator for the shape parameter ξ {\displaystyle \xi ...
The two generalized normal families described here, like the skew normal family, are parametric families that extends the normal distribution by adding a shape parameter. Due to the central role of the normal distribution in probability and statistics, many distributions can be characterized in terms of their relationship to the normal ...