# Wydawnictwa / Czasopisma IMPAN / Applicationes Mathematicae / Wszystkie zeszyty

## A model for proportions with medical applications

### Tom 34 / 2007

Applicationes Mathematicae 34 (2007), 15-27 MSC: 33C90, 62E99. DOI: 10.4064/am34-1-2

#### Streszczenie

Data that are proportions arise most frequently in biomedical research. In this paper, the exact distributions of $R = X + Y$ and $W = X/(X + Y)$ and the corresponding moment properties are derived when $X$ and $Y$ are proportions and arise from the most flexible bivariate beta distribution known to date. The associated estimation procedures are developed. Finally, two medical data sets are used to illustrate possible applications.