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

 SechDistributionrepresents the hyperbolic secant distribution with location parameter and scale parameter .
• The probability density for value in a hyperbolic secant distribution is proportional to .
• SechDistribution allows to be any real number and to be any positive real number.
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   (6)
Generate a set of pseudorandom numbers that are hyperbolic secant distributed:
Compare its histogram to the PDF:
Distribution parameters estimation:
Estimate the distribution parameters from sample data:
Compare a density histogram of the sample with the PDF of the estimated distribution:
Skewness and kurtosis are constant:
Different moments with closed forms as functions of parameters:
Closed form for symbolic order:
Closed form for symbolic order:
Hazard function:
Quantile function:
 Applications   (1)
SechDistribution is an envelope of a soliton wave. Find the full width at half maximum:
Parameter influence on the CDF for each :
Sech distribution is closed under translation and scaling by a positive factor:
The PDF of SechDistribution is bell-shaped, similar to NormalDistribution:
The tails of SechDistribution are lighter than those of NormalDistribution:
Mean and variance:
Hyperbolic secant distribution mimics LogisticDistribution:
Compare the histogram to the PDF of the estimated distribution:
Comparing the fit with original distribution:
New in 8