## Abstract

A magazine-exposure model that mixes Klotz’s (1973) dependent Bernoulli-trials model for nonsubscribers with a degenerate distribution for subscribers is proposed. Let X_{i} = 1 if a person reads an issue of a particular magazine and 0 otherwise. Klotz’s parameterization is Pr(X_{i} = 1) = p and Pr(X_{i} = 1 ∣X_{i–1} = 1) = λ for i = 1, …, k. Using the Markov assumption he obtains the joint distribution of (Equation presented), and T = X_{1} + X_{k}, of which we are interested in the marginal distribution of S, the total number of issues a person reads. It is expected that p will be low for nonsubscribers but high for subscribers, so this heterogeneity is modeled by mixing Klotz’s Markov model with a point mass of magnitude π at the point S = k. Maximum likelihood estimates of p, λ, and π are used to fit the Markov mixture model to 40 magazines from a large print-media survey. The proposed model is shown to give a much better fit to these data than the beta-binomial model, the most popular nonproprietary magazine model, and a generalization of the beta-binomial model.

Original language | English |
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Pages (from-to) | 922-926 |

Number of pages | 5 |

Journal | Journal of the American Statistical Association |

Volume | 84 |

Issue number | 408 |

DOIs | |

Publication status | Published - 1 Jan 1989 |

Externally published | Yes |

## Keywords

- Beta-binomial model
- Magazine-exposure distribution
- Markov chain
- Modified beta-binomial model