Similarly, truncation from above means the exact value of
[2] Truncation is similar to but distinct from the concept of statistical censoring.
Usually the values that insurance adjusters receive are either left-truncated, right-censored, or both.
For example, if policyholders are subject to a policy limit u, then any loss amounts that are actually above u are reported to the insurance company as being exactly u because u is the amount the insurance company pays.
The insurer knows that the actual loss is greater than u but they don't know what it is.
On the other hand, left truncation occurs when policyholders are subject to a deductible.
If policyholders are subject to a deductible d, any loss amount that is less than d will not even be reported to the insurance company.
Therefore, insurance loss data is left-truncated because the insurance company doesn't know if there are values below the deductible d because policyholders won't make a claim.
in the modified density function which will depend on the parameters of the original distribution.
In such cases, a truncated or censored version of the normal distribution may formally be preferable (although there would be alternatives); there would be very little change in results from the more complicated analysis.
[4] Regression models with such dependent variables require special care that properly recognizes the truncated nature of the variable.
Estimation of such truncated regression model can be done in parametric,[5][6][7] or semi- and non-parametric frameworks.