I have data for an experiment that aims to check how good a machine is in detecting flaws in structures.
The Probability of Detection is a function of the flaw size and some other environmental factors. I have 70 measurements points summarized in the table below, where I have the flaw size, and if the flaw was detected or not (0 or 1).
From this data, we can plot those points as shown in the figure below (triangular points). However, I am interested in getting the fitted curve from the data points. The probability of detection is a function of flaw size. According to the reference, I am reading from the probability density function can be written as below: where a is the size of the flaw, mu and sigma are the mean and the standared deviation respectively, B0 and B1 are functions of the mean and the standard deviation. Using logistic regression in R or minitab, B0 and B1 can be estimated.
I am interested in working out this calculation myself and write my own code for that, in other words, I am interested in the algorithm that will allow me to estimate the parameters to draw the fitted curve.