Ratio Estimators and Some Inherent Problems in Their Utilization

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  • 1 Department of Statistics, Temple University, Philadelphia, Pa. 19122
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Abstract

Ratio estimators are widely utilized in the physical and atmospheric sciences, although their properties and inherent problems are often unknown or overlooked. A number of problems and properties of ratio estimators are presented and some solutions are offered. For a correlated bivariate gamma structure, approximate and exact results are given for the mean, variance and biases of the ratio of two means. The sensitivity of these results to sample size and parameters of the bivariate gamma are indicated. The application of these results to three well-known cloud seeding experiments are presented and “corrected” estimates of the corresponding seeding effects are offered.

Abstract

Ratio estimators are widely utilized in the physical and atmospheric sciences, although their properties and inherent problems are often unknown or overlooked. A number of problems and properties of ratio estimators are presented and some solutions are offered. For a correlated bivariate gamma structure, approximate and exact results are given for the mean, variance and biases of the ratio of two means. The sensitivity of these results to sample size and parameters of the bivariate gamma are indicated. The application of these results to three well-known cloud seeding experiments are presented and “corrected” estimates of the corresponding seeding effects are offered.

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