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L. LeCam, “A Stochastic Description of Precipitation,” 4th Berkeley Symposium on Mathematical Statistics and Probability, Statistical Laboratory of the University of California, Berkeley, 20 June-30 July 1960, pp. 165-186.

has been cited by the following article:

• TITLE: Simulation of a Daily Precipitation Time Series Using a Stochastic Model with Filtering

  AUTHORS: Chieko Gomi, Yasuhisa Kuzuha

  KEYWORDS: e-Model; Daily Precipitation Time Series; Filtering; Fractional Brownian Motion; Fractional Lévy Motion; Stochastic Model

  JOURNAL NAME: Open Journal of Modern Hydrology, Vol.3 No.4, October 23, 2013

  ABSTRACT: After we modified raw data for anomalies, we conducted spectral analysis using the data. In the frequency, the spectrum is best described by a decaying exponential function. For this reason, stochastic models characterized by a spectrum attenuated according to a power law cannot be used to model precipitation anomaly. We introduced a new model, the e-model, which properly reproduces the spectrum of the precipitation anomaly. After using the data to infer the parameter values of the e-model, we used the e-model to generate synthetic daily precipitation time series. Comparison with recorded data shows a good agreement. This e-model resembles fractional Brown motion (fBm)/fractional Lévy motion (fLm), especially the spectral method. That is, we transform white noise Xt to the precipitation daily time series. Our analyses show that the frequency of extreme precipitation events is best described by a Lévy law and cannot be accounted with a Gaussian distribution.