Normal Distribution Equation

Link to Normal Distribution Explanation

Base equation for derivation of normal distribution function:
ΔS/S ~ φ(μ Δt, θ√Δt)

Calculation of mean return and standard deviation with lognormal distribution:
ln ST ~ φ[ lnS0 + (μ – θ2/2)T, θ√T ]

Calculation of standard deviation intervals:
e(μ-s*θ) < ln ST < e(μ+s*θ)

Where  μ is the mean of ln ST, s is the # of std dev from the mean, and θ is the std dev of ln ST.

Link to Example: Normal Distribution Calculations

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