Suppose X is some random varable. The probability distribution of X, conditional on X > c, is called "the left-truncated distribution of X, truncated at c". If X has a probability density, then the left-truncated distribution also has a density or mass-function, and it equals that of X, restricted to x > c, and normalized to have total mass 1.
One can of course similarly define truncation on the right, or even truncation on both sides.
Suppose X is some random varable. The probability distribution of X, conditional on X > c, is called "the left-truncated distribution of X, truncated at c". If X has a probability density, then the left-truncated distribution also has a density or mass-function, and it equals that of X, restricted to x > c, and normalized to have total mass 1.
One can of course similarly define truncation on the right, or even truncation on both sides.
The answer by Richard Gill is correct. That is how truncation is performed.
A reason for truncation may be that there is no interest beyond the truncation point. Truncate and normalize as long as the distribution is a good description of the data.
Another reason for truncation is that the distribution is not valid beyond the truncation point. For example, a Normal distribution extends below zero, but negative values are not possible. Truncation will introduce an error, but it may be small enough to ignore. When the error cannot be ignored or you suspect it cannot be ignored, use a more appropriate distribution. A Gamma distribution will cut off at zero, while a Beta distribution will have upper and lower limits. The best distribution is one that theoretically follows the mechanics of the process.
Suppose we have a random variable, X {\displaystyle X} 📷 that is distributed according to some probability density function, f ( x ) {\displaystyle f(x)} 📷, with cumulative distribution function F ( x ) {\displaystyle F(x)} 📷 both of which have infinite support. Suppose we wish to know the probability density of the random variable after restricting the support to be between two constants so that the support, y = ( a , b ] {\displaystyle y=(a,b]} 📷. That is to say, suppose we wish to know how X {\displaystyle X} 📷 is distributed given a < X ≤ b {\displaystyle a
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