This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# CensoredDistribution

 CensoredDistribution represents the distribution of values that come from dist and are censored to be between and . CensoredDistributionrepresents the distribution of values that come from the multivariate distribution dist and are censored to be between and , and , etc.
• Common cases for include:
 {-∞,xmax} censoring from above, right-censoring {xmin,∞} censoring from below, left-censoring {xmin,xmax} doubly censored, interval-censoring {-∞,∞},None no censoring, uncensored
Define a left-censored discrete distribution:
Probability density function:
Define a right-censored continuous distribution:
Cumulative distribution function:
Define a left-censored discrete distribution:
Probability density function:
 Out[2]=

Define a right-censored continuous distribution:
Cumulative distribution function:
 Out[2]=
 Scope   (25)
Define different types of censoring for a univariate discrete distribution:
Define different types of censoring for a univariate continuous distribution:
Define a right-censored discrete distribution:
Compare probability density functions:
Find probability at 9 for the censored distribution:
Compare to the probability of obtaining a value of at least 9 for the original distribution:
Censoring of continuous distributions results in the PDF having generalized functions:
Use a histogram and plot the original density function to visualize the point probability:
The value of the PDF at the truncation point:
A distribution censored to one point:
Censoring for a multivariate continuous distribution:
Compute the expectation of an expression for this distribution:
Censoring for a multivariate discrete distribution:
Compute the mean for the distribution:
Compare with the result obtained using a random sample drawn from the distribution:
Define a doubly censored distribution:
Cumulative distribution function:
The mean and variance of the censored distribution:
Moment has closed form for symbolic order:
Estimate the censoring interval:
Define a right-censored continuous distribution:
Probability density function:
Plot a histogram for a random sample. The spike corresponds to the DiracDelta part of PDF:
Define a censored GeometricDistribution:
Compare probability density functions:
The values of the PDF at the censoring points are equal to the following probabilities:
Find generating functions:
Define a right-censored PoissonDistribution:
Define a two-dimensional censored DirichletDistribution:
Compare CDFs:
Mean and variance for the censored distribution:
Compute probabilities and expectations:
Define a censored EmpiricalDistribution:
Compare cumulative distribution functions:
Define a censored HistogramDistribution:
Compare CDFs:
Define a censored SmoothKernelDistribution:
Compare cumulative distribution functions:
Define a censored ParameterMixtureDistribution:
Cumulative distribution function:
Define a censored MixtureDistribution:
Cumulative distribution function:
Define a a censored OrderDistribution:
Probability density function:
Compare means:
Define a censored CensoredDistribution:
Probability density function:
Compare to doubly censored Poisson distribution:
Define a censored TruncatedDistribution:
Compare cumulative distribution functions:
Define a censored TransformedDistribution:
Probability density function:
Define a censored MarginalDistribution:
Probability density function:
Compare with the PDF of the marginal:
Define a censored ProductDistribution:
Visualize the density function using a random sample:
 Applications   (4)
An insurance company buys reinsurance at retention level . Assuming claims follow lognormal distribution, find moments of insurer's payout random variate:
Find moments of reinsurer's payout random variate:
The lifetime of a component follows a RayleighDistribution. The components are tested for failures for hours and if a component has not failed it is assumed to have the lifetime of exactly hours. Find the length of the test so that at most 5% of the tested components have a lifetime longer than :
Find the test lifetime distribution for :
Compare the censored distribution with the actual lifetime distribution:
The number of shots a beginner golf player needs to sink a 4-par hole follows a PoissonDistribution with an average of 9 shots. Assuming that on the golf course he picks the ball after the tenth shot, find the distribution of the number of shots on a 4-par hole:
Probability density function:
The average number of shots per 4-par hole on the golf course:
Find the probability that he needs more than 4 shots to sink the ball:
The body weight of adult males in the U.S. follows a normal distribution with a mean of 191 lbs and a standard deviation of 70 lbs. Assuming that each bathroom scale has an upper limit of 300 lbs, find the weight distribution when the measurements are done with a generic bathroom scale:
Cumulative distribution function:
Visualize the density function with a random sample:
Find the average weight:
Find the probability of weighing at least 200 lbs:
Find the probability of weight at or above the scale limit:
Compare to the uncensored distribution:
Compare censoring with truncating for a discrete distribution:
While censoring, the weight from outside is placed at the ends of the censoring interval:
While truncating, the weight from outside is evenly distributed over the truncation interval:
Compare censoring and truncating of a continuous distribution:
While censoring, the probability is put at the end of the censoring interval:
While truncating, the probability is distributed over the truncation interval:
New in 8