Fitting Normal Distributions to Apple Fruit and its Application

Jianlu Zhang                        Alan Robson           
Agriculture New Zealand     Asure New Zealand
Private Bag 9024                 PO Box 1141          
Hastings                               Christchurch           
New Zealand                        New Zealand          

Abstract. Orchardists' income is determined by the entire fruit size distribution at harvest, not just mean fruit size. Testing goodness-of-fit of the normal distribution of apple fruit size is useful for model development. From 1993 to 1999, 272 apple trees were selected comprising 5 varieties in 2 regions in New Zealand. For these 272 trees, every individual fruit was weighed and recorded on a tree basis. Goodness-of-fit tests based on normal distribution were conducted on a tree basis using the Anderson-Darlings statistic. Fruit sized distributions of 172 trees fit a normal curve within a 5% level. Five trees failed the normal distribution test due to just one outlying fruit and 15 trees failed the test due to fewer than five outlying fruit. Thirty-seven trees failed the test at the extremities of the size range and 43 trees failed the fit for the entire size range. Skewness tests showed that 154 trees did not reach a significant level for skewness and 36 trees failed the skewness test due to a single fruit. Eighty-nine trees had positive skewness (a peak of small fruit size and a tail of large fruit size) and 29 trees had negative skewness. Kurtosis tests showed that 200 trees did not reach a significant level for kurtosis and 24 trees failed only due to 1 fruit. Sixty-six trees had kurtosis coefficients > 3 (actual distributions are wider than normal distribution) and 6 trees had kurtosis coefficients < 3. This work demonstrated the relationship between fruit weight and its standard deviation and the usage of coefficient of variance (CV). The CV was dependent on variety (16% to 28%). Chemical and hand thinning reduced the CV of Royal Gala fruit weight. In addition, ¡°size¡± hand thinning further reduced the CV. Results from the New Zealand national crop estimate were accurate for each countsize.

Keywords Malus domestica, normality, fruit size distribution, skewness, kurtosis

from Acta Horticulturae. 584: 169-175.