what is the difference between bottom up estimation and parametric estimation.

One obvious difference is that parametric est. depends of historical information, anything more....
Could anyone clarify ?

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That is the key difference. Bottom up estimation is when you estimate for each work package and then roll up to get final estimate. In parametric estimation you check for historical records to see that a project of X size took Y Months. So project of 2X size would take 2Y months. Calculation may not necessarily be linear, it can be any extrapolation

However the key confustion is between parameteric and analogus estimate. In Parametric estimation , historical data is used for extrapolating or calculating, in analogus estimate its more of judgement call based on similar projects done in past.