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

 LindleyDistribution[] represents a Lindley distribution with shape parameter .
• The probability density for value is proportional to for , and is zero for .
Probability density function:
Cumulative distribution function:
Mean and variance:
Median:
Probability density function:
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Cumulative distribution function:
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Mean and variance:
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Median:
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 Scope   (7)
Generate a set of pseudorandom numbers that are Lindley distributed:
Compare its histogram to the PDF:
Distribution parameters estimation:
Estimate the distribution parameters from sample data:
Compare the density histogram of the sample with the PDF of the estimated distribution:
Skewness depends on the shape parameter :
Limiting values:
Kurtosis depends on the shape parameter :
Limiting values:
Different moments with closed forms as functions of parameters:
Closed form for symbolic order:
Closed form for symbolic order:
Closed form for symbolic order:
Hazard function:
Quantile function:
 Applications   (2)
LindleyDistribution is used to create a discrete Poisson-Lindley distribution:
Probability density function:
Cumulative distribution function:
Mean is the same as for LindleyDistribution:
Poisson-Lindley distribution can be used to model insurance claim counts:
Estimate parameters based on claim amounts:
The fit is better than using just PoissonDistribution:
Parameter influence on the CDF for each :
New in 8