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In statistics, a truncated distribution is a conditional distribution that results from restricting the domain of some other probability distribution.Truncated distributions arise in practical statistics in cases where the ability to record, or even to know about, occurrences is limited to values which lie above or below a given threshold or within a specified range.
In probability and statistics, the truncated normal distribution is the probability distribution derived from that of a normally distributed random variable by bounding the random variable from either below or above (or both). The truncated normal distribution has wide applications in statistics and econometrics.
Truncation can be applied to any probability distribution.This will usually lead to a new distribution, not one within the same family. Thus, if a random variable X has F(x) as its distribution function, the new random variable Y defined as having the distribution of X truncated to the semi-open interval (a, b] has the distribution function
The triangular distribution on [a, b], a special case of which is the distribution of the sum of two independent uniformly distributed random variables (the convolution of two uniform distributions). The trapezoidal distribution; The truncated normal distribution on [a, b]. The U-quadratic distribution on [a, b].
A truncated mean or trimmed mean is a statistical measure of central tendency, much like the mean and median. It involves the calculation of the mean after discarding given parts of a probability distribution or sample at the high and low end, and typically discarding an equal amount of both.
Consider the truncated distribution defined by restricting the standard Cauchy distribution to the interval [−10 100, 10 100]. Such a truncated distribution has all moments (and the central limit theorem applies for i.i.d. observations from it); yet for almost all practical purposes it behaves like a Cauchy distribution. [16]
where () is a truncated probability distribution function, truncated at 0. Hurdle models were introduced by John G. Cragg in 1971, [1] where the non-zero values of x were modelled using a normal model, and a probit model was used to model the zeros.
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