Bayesian estimation of Huff curves

We propose a nonparametric Bayesian method for estimating regression functions that arise as cumulative distribution functions (cdfs) of a stochastically ordered family of distribution supported on [0,1]. The motivating example is estimation of Huff curves which are depth duration curves for heavy storm rainfall. The Bayesian methodology is compared with the linear programming based estimation method that is currently used by the national Oceanic and Atmospheric Administration (NOAA) for producing the Huff curves. The methodology is illustrated with the rainfall data from the rain gauge stations in California, US. Some limited simulation results are provided to illustrate the finite sample performance of the proposed estimator. We also establish consistency of the proposed method.