Application of the Incomplete Gamma Function to Predict Cumulative Milk Production

Abstract

The incomplete .gamma. function was used to generate lactation curves for a large sample of Holstein records from the Northeast Dairy Herd Improvement Association files. Curves were fitted by linear regression on the log transformation of the incomplete .gamma. function. Effects of month of freshening, days open, and intra- and interherd variability in cumulative yield were determined separately by linear regression for 1st, 2nd and later lactations for each parameter of the model. These predictions were used to extend partial records of milk production to 305 day equivalent. Predicted effects of parity number and season of freshing on incomplete .gamma. parameters b and c were used to specify shape of the lactation curve for partial records. Since most variation in lactation curves for high and low producing cows was due to variation in the equation multiplier, this parameter was changed to shift the predicted curve closer to observations in the partial records. Predictions of 305 day cumulative yield from partial records by this technique had smaller root mean squares (356-586 kg) than the test interval method with extension factors (396-751 kg).