I am trying to measure the amount of compounds by the peak area and I want to increase accuracy to 0.1% by curve fitting. Can I do it and what functions should I use?
Yes, you can curve fit all three of them. For NMR use lorentzian shape.For other two use Gaussian peak shape.
But remember: measurements in chemistry are typically 10% accurate. Increasing accuracy beyond that is difficult.
Mass-spectrometry is only quantitative if you study isotopic molecules. You cannot compare alcohol with an acid and amine using MS. Amine will dominate in positive mode and acid will dominate in negative mode.
GC is the most reliable but you have to find the right dose. Not to small, so that your peak is visible, and not to high to avoid asymmetry. Tecknically, you can use asymmetric fitting curve, but those fits are less stable (less reliable, even though the R is better).
You should not assume any given peak shape as in practice this may not be what it should be from theory.
You have a set of data points so once you have determined the baseline a numerical integration should work well. There are many of these in the literature. When fitting use the chi squared statistic as a measure of fit, the Pearson R is just useless and should never be used in fitting. (This is because a poor fit has, say, an R = .99 and a good fit .999 so its not anywhere near discriminating enough). You should also look at the shape of the residuals, autocorrelation function, runs tests etc to make sure you have a good fit. A one parameter good/bad test is often not good enough.
If you have overlapping peaks then you will have to assume some shape simply to use non-linear least squares to estimate one peak from another. This will lead to some more uncertainty but depending on what you are trying to determine this may not matter.
In gc data the peak shape is not necessarily gaussian, often it is lopsided so a numerical method is better here.
It may not be necessary to fit your data to try to get such high precision, the data simply may not allow it due to instrumental factors. But what is important is results not data, i.e. its what the data tells you that is important; this may not need such high precision as you seek. I'm absolutely not being patronising, but I would go as far as to say that if you need 0.1% accuracy you should perhaps think of another way of trying to learn what you want to know.