### Abstract

To estimate the mean sojourn time, a sample of Tilburg fair visitors was asked for the duration of their stay on the fair grounds. The longer a visitor's sojourn, the larger his/her probability of being interviewed will be; therefore, longer sojourn times will be overrepresented in the sample. As a consequence, the arithmetic sample mean is not a suitable estimator. The paper places this problem against a theoretical background. As a better estimator the harmonic mean of the observed sojourn times is presented. In addition, a variance estimator is given. The properties of these estimators are difficult to derive analytically. Instead, their behaviour is studied in a number of examples.

Original language | English |
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Publisher | Unknown Publisher |

Number of pages | 15 |

Volume | FEW 717 |

Publication status | Published - 1996 |

### Publication series

Name | Research memorandum / Tilburg University, Faculty of Economics and Business Administration |
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Volume | FEW 717 |

### Keywords

- Probability
- Estimation
- Sampling
- statistics

## Fingerprint Dive into the research topics of 'Sampling with probabilities proportional to the variable of interest'. Together they form a unique fingerprint.

## Cite this

Moors, J. J. A., Smeets, R., & Boekema, F. W. M. (1996).

*Sampling with probabilities proportional to the variable of interest*. (Research memorandum / Tilburg University, Faculty of Economics and Business Administration; Vol. FEW 717). Unknown Publisher.