BUILT-IN MATHEMATICA SYMBOL

CensoredDistribution

represents the distribution of values that come from dist and are censored to be between

and

.

CensoredDistribution

represents the distribution of values that come from the multivariate distribution dist and are censored to be between

and

,

and

, etc.

MORE INFORMATION

CensoredDistribution is equivalent to TransformedDistribution, where f is given by Piecewise.

Common cases for include:

	{-∞,x_max}	censoring from above, right-censoring
	{x_min,∞}	censoring from below, left-censoring
	{x_min,x_max}	doubly censored, interval-censoring
	{-∞,∞},None	no censoring, uncensored

CensoredDistribution can be used with such functions as Mean, CDF, RandomVariate, etc.

EXAMPLES

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Basic Examples (2)

Define a left-censored discrete distribution:

Probability density function:

Define a right-censored continuous distribution:

Cumulative distribution function:

Define a left-censored discrete distribution:

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Probability density function:

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Define a right-censored continuous distribution:

In[1]:=

Cumulative distribution function:

In[2]:=

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:

Define a doubly censored GammaDistribution:

Find generating functions:

Define a right-censored PoissonDistribution:

Compare HazardFunction:

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:

Compare the average lifetimes:

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:

Properties & Relations (3)

CensoredDistribution is a special case of TransformedDistribution:

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: