Fitting the generalized lambda distribution to pre-binned data

Abstract

Density estimation for pre-binned data is challenging due to the loss of exact position information of the original observations. Traditional kernel density estimation methods cannot be applied when data are pre-binned in unequally spaced bins or when one or more bins are semi-infinite intervals. We propose a novel density estimation approach using the generalized lambda distribution (GLD) for data that have been pre-binned over a sequence of consecutive bins. This method enjoys the high power of the parametric model and the great shape flexibility of the GLD. The performances of the proposed estimators are benchmarked via simulation studies. Both simulation results and a real data application show that the proposed density estimators work well for data of moderate or large sizes.

Keywords:

• top-coded data
• maximum likelihood method
• model fitting
• binned data
• histogram

AMS Subject Classification:

• 62F86
• 65G40
• 65G50
• 97N20

Disclosure statement

No potential conflict of interest was reported by the authors.