## 1 Introduction

[2] Rainfall frequency analysis is used for constructing intensity-duration-frequency (IDF) curves, which are needed for a range of hydrologic designs, including drainage systems, culverts, roadways, parking lots, runways, and so on. Extreme rainfall values, such as annual rainfall maxima, are of interest in modeling floods and quantifying the effect of climate change. From the fitted distribution, statistical properties of extreme rainfall values can be investigated and extrapolated beyond the available data for engineering purposes.

[3] The generalized extreme value (GEV) distribution is one of the frequently employed probability distributions for modeling and characterizing extreme values. Derived from the extreme value theory, it is a three-parameter distribution encompassing three classes of distributions, namely, Gumbel, Frechet, and Weibull. This distribution has been used for extreme rainfall frequency analysis in different areas of the world. *Schaefer* [1990] used the GEV distribution for frequency analysis of annual rainfall maxima of durations of 2, 6, and 24 hours for the state of Washington. *Huff and Angel* [1992] selected the GEV distribution to model the distribution of annual rainfall maxima for durations from 5 minutes to 10 days in the mid-western United States. *Parrett* [1997] also used the GEV distribution to construct dimensionless frequency curves of annual rainfall maxima of durations of 2, 6, and 24 hours within each region in Montana. Using the L-moment ratio diagram, *Asquith* [1998] determined that the GEV distribution was an appropriate distribution for modeling the distribution of annual rainfall maxima for durations from 1 to 7 days. *Alila* [1999] showed that the annual rainfall maxima of durations from 5 minutes to 24 hours in Canada were better described by the GEV distribution than other distributions, such as the generalized logistic and EV1 distributions.

[4] Extreme rainfall exhibits different properties for different durations in different regions. Analysis of rainfall characteristics is important for choosing a suitable rainfall distribution and consequently estimating rainfall quantiles. Therefore, the objective of this study is to investigate the change in the form of the annual rainfall maxima frequency distribution with changes in the time duration, climate zone, and distance from the Gulf of Mexico and then derive an entropy-based distribution that is sufficiently flexible for characterizing rainfall distributions for different durations in different climatic zones or at different distances from the Gulf of Mexico. The performance of the proposed entropy-based distribution is assessed using synthetic data through Monte Carlo simulation and observed rainfall data and is shown to be a promising alternative distribution to the commonly used GEV distribution for modeling extreme rainfall values, especially observations with high skewness.

[5] This article is organized as follows. In section 2, the change in the form of empirical distributions of annual rainfall maxima is investigated. Using the entropy theory, a generalized distribution is derived in section 3 and the performance of this distribution is assessed by comparing the GEV distribution in section 4. After the application of the proposed entropy-based distribution in section 5, conclusions are given in section 6.