Estimation of standard error of impedance‐estimated frost resistance

Abstract

The magnitude of measurement errors of the specific impedance difference was estimated and a formula to approximate the variance of the estimated frost resistance was derived. The measurements of specific impedance difference include the measurement errors of impedance before and after frost treatment and cross-sectional area. These errors in connection with the population variation cause variation in the estimated frost resistance. The frost resistance is estimated by first expressing the specific impedance difference values as a logistic sigmoid function of the treatment temperature, and then evaluating the inverse function at a given value of the specific impedance difference. The error variance between the estimated and the measured frost resistance was calculated using the estimated parameters, their standard deviations and correlations. In an example the impedance estimated frost resistance (LT.i0Qm) was - 10.9°C and its standard deviation 0.8°C.

Key words:

• Gauss-Newton
• inverse function
• nonlinear regression
• logistic sigmoid