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Estimation of Mean Rain Rate through Censoring

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  • 1 Mathematics Department, Howard University, Washington, D.C.
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Abstract

A mixed lognormal distribution is fit to rain-rate data to estimate the space–time average. To mitigate problems associated with biased data, data below a minimum and above a maximum threshold are treated as if they are at the respective threshold, and thus in a sense, are censored. The asymptotic variability of the estimate is computed using Fisher information. Computations of asymptotic variance over a portion of the parameter space show that estimates from censored data are more efficient than those from the minimum chi-square and least squares methods. The censoring, minimum chi-square, and least square methods are applied to simulated data to illustrate their usefulness in estimating rain rate.

Corresponding author address: Donald Martin, Mathematics Department, Howard University, Washington, DC 20059.

demartin@fac.howard.edu

Abstract

A mixed lognormal distribution is fit to rain-rate data to estimate the space–time average. To mitigate problems associated with biased data, data below a minimum and above a maximum threshold are treated as if they are at the respective threshold, and thus in a sense, are censored. The asymptotic variability of the estimate is computed using Fisher information. Computations of asymptotic variance over a portion of the parameter space show that estimates from censored data are more efficient than those from the minimum chi-square and least squares methods. The censoring, minimum chi-square, and least square methods are applied to simulated data to illustrate their usefulness in estimating rain rate.

Corresponding author address: Donald Martin, Mathematics Department, Howard University, Washington, DC 20059.

demartin@fac.howard.edu

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