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SechDistribution

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Hyperbolic secant distribution (Sech PDF and ArcTan CDF)

SechDistribution[μ, σ]
SechDistribution[]
Mean[SechDistribution[μ, σ]] → μPDF[SechDistribution[μ, σ], x] → Sech[(Pi*(x - μ))/(2*σ)]/(2*σ)CDF[SechDistribution[μ, σ], x] → (2*ArcTan[E^((Pi*(x - μ))/(2*σ))])/Pi
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