# Density Estimation from GROuped Summary Statistics

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 ddegross Density function based on an object resulting from the estimation procedure in degross. degross Density estimation from tabulated data with given frequencies and group central moments. degross.object Object resulting from the estimation of a density from grouped (tabulated) summary statistics degrossData Creates a degrossData.object from the observed tabulated frequencies and central moments. degrossData.object Object generated from grouped summary statistics, including tabulated frequencies and central moments of order 1 up to 4, to estimate the underlying density using 'degross'. degross_lpost Log-posterior (with gradient and Fisher information) for given spline parameters, small bin frequencies, tabulated sample moments and roughness penalty parameter. This function is maximized during the M-step of the EM algorithm to estimate the B-spline parameters entering the density specification. degross_lpostBasic Log-posterior for given spline parameters, big bin (and optional: small bin) frequencies, tabulated sample moments and roughness penalty parameter. Compared to degross_lpost, no Fisher information matrix is computed and the gradient evaluation is optional, with a resulting computational gain. pdegross Cumulative distribution function (cdf) based on an object resulting from the estimation procedure in degross. plot.degross Plot the density estimate obtained from grouped summary statistics using degross and superpose it to the observed histogram. print.degross Print a 'degross' object. print.degrossData Print a 'degrossData' object. qdegross Quantile function based on an object resulting from the estimation procedure in degross. Sigma_fun Variance-covariance of sample central moments (root-n approximation) given the vector mu with the theoretical moments of order 1 to 8. CAREFUL: the result must be divided by n (= sample size)! simDegrossData Simulation of grouped data and their sample moments to illustrate the degross density estimation procedure