Describing fruit size distributions is important in horticultural research. Early season size distributions are of special interest because these can form the basis for developing predictive models that project forward initial size distributions to harvest. Size monitoring of apple crop during the growing season is usually done by nondestructive measurement of fruit diameters and, such data are often nonnormal and skewed. In this study we demonstrate the use of Johnson's S_B density to model fruit diameters at several points in time during fruit growth. The motivation for using Johnson's S_B came from several other studies that found S_B to be more flexible for modelling forest tree characteristics that exhibited both positive and negative skewness. Most papers in the literature deal with percentile and end-point methods for estimation of S_B parameters. These methods gave poor fits to our data. We propose a maximum likelihood method based on simultaneously optimizing for all four parameters of the S_B density function using standard optimization routines. The S_B density function fitted the diameter data only at early season measurement times. In contrast, the lognormal distribution fitted reasonably well at all stages through to harvest. In this article we also discuss the implications of accurate description of early season size distribution on methods for predicting harvest fruit size distribution.

Key Words
Fruit size distribution; Johnson distribution; Maximum likelihood.

H. Nihal De Silva is Biometrician, The Horticulture and Food Research Institute of New Zealand, Private bag 11030, Palmerston North, New Zealand. C. D. Lai is Senior Lecturer in Statistics, Department of Statistics, Massey University, Palmerston North, New Zealand. Roderick D. Ball is Statistician, New Zealand Forest Research Institute, Private Bag 3020, Rotorua, New Zealand.