### Abstract

This paper introduces two general models for computing centiles when the response variable Y can take values between 0 and 1, inclusive of 0 or 1. The models developed are more flexible alternatives to the beta inflated distribution. The first proposed model employs a flexible four parameter logit skew Student t (logitSST) distribution to model the response variable Y on the unit interval (0, 1), excluding 0 and 1. This model is then extended to the inflated logitSST distribution for Y on the unit interval, including 1. The second model developed in this paper is a generalised Tobit model for Y on the unit interval, including 1. Applying these two models to (1-Y) rather than Y enables modelling of Y on the unit interval including 0 rather than 1. An application of the new models to real data shows that they can provide superior fits.

Lingua originale | English |
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pagine (da-a) | 895-904 |

Numero di pagine | 10 |

Rivista | Statistics in Medicine |

Volume | 35 |

Stato di pubblicazione | Published - 2016 |

### All Science Journal Classification (ASJC) codes

- Epidemiology
- Statistics and Probability

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## Cita questo

Enea, M., Stasinopoulos, M., Hossain, A., & Rigby, R. (2016). Centile estimation for a proportion response variable.

*Statistics in Medicine*,*35*, 895-904.