Truncated Midzuno–Sen Sampling Schemes for Estimating Distribution Functions

We consider a truncated Midzuno–Sen sampling scheme. The proposed method can be used to estimate the distribution function of a study variable assuming that the distribution function of an auxiliary variable is known. The ratio estimator for estimating the distribution function is shown to remain unbiased. We introduce the first- and second-order inclusion probabilities under the truncated Midzuno–Sen sampling scheme. Numerical examples are provided to support our theoretical results.

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