It depends on exactly what you mean by "best fitting curve". In general, there is certainly no guarantee that the best-fitting parameters for each distribution (e.g., by maximum likelihood) will give you means that match the means in your data. You will see even bigger discrepancies if you check the standard deviations of the distributions against the standard deviation in your data (e.g., for the exponential). Your only option is to pick your optimization criterion (e.g., maximum likelihood); once you do that, you just have to live with the discrepancies in predicted/observed means, standard deviations, etc. If you really want to match those and don't care about likelihood, you can use the method of moments for your optimization criterion, but the estimates obtained with that method don't generally have nice statistical properties.
Hope that helps.
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