Density Estimation using Entropy Maximization for Semi-continuous Data

TL;DR

This paper introduces a new maximum entropy-based algorithm for estimating the density of semi-continuous data, such as rainfall, which requires only sample constraint values and demonstrates reduced bias in simulations.

Contribution

The novel algorithm simplifies density estimation for semi-continuous data by using only sample constraint values and improves bias performance over existing methods.

Findings

Reduced bias in entropy estimates compared to existing methods

Effective density estimation for rainfall data

Algorithm requires only sample constraint values

Abstract

Semi-continuous data comes from a distribution that is a mixture of the point mass at zero and a continuous distribution with support on the positive real line. A clear example is the daily rainfall data. In this paper, we present a novel algorithm to estimate the density function for semi-continuous data using the principle of maximum entropy. Unlike existing methods in the literature, our algorithm needs only the sample values of the constraint functions in the entropy maximization problem and does not need the entire sample. Using simulations, we show that the estimate of the entropy produced by our algorithm has significantly less bias compared to existing methods. An application to the daily rainfall data is provided.