sd = estimated standard scattering factor sigma deisenroth (geschätzter standardstreufaktor sigma deisenroth)

sd = e^(2*ln(xari/xgeo)^0,5 = estimated standard scattering factor sigma deisenroth

true arithmetic mean (µari) and true geometric mean (µgeo)

µari = true arithmetic mean (wahrer arithmetischer mittelwert)

µgeo = true geometric mean (wahrer geometrischer mittelwert)

µari = µgeo*e^(0,5*ln(σd)^2)

µgeo or µ = µari/e^(0,5*ln(σd)^2) ≠ µari for phi factor and phi density normal distribution

estimated arithmetic mean (xari) and estimated geometric mean (xgeo)

xari = estimated arithmetic mean (geschätzter arithmetischer mittelwert)

xgeo = estimeted geometric mean (geschätzter geometrischer mittelwert)

xgeo(x_i;n) = e^(1/n*((ln(x₁)+ln(x₂)+.....+ln(x_n)))

xgeo(sd;xari) = xari/e^(0,5*ln(sd)^2)

xari(x_i;n) = 1/n*(x₁+x₂+ ....+x_n)

xari(sd;xgeo) = xgeo*e^(0,5*ln(sd)^2)

true standard scattering factor sigma deisenroth σd and estimated standard scattering factor sigma deisenroth sd

σd = true standard scattering probability limit factor sigma deisenroth (wahrer standardstreufaktor sigma deisenroth)

sd = estimated standard scattering probability limit factor sigma deisenroth (geschätzter standardstreufaktor sigma deisenroth)

σd or σ = e(2*ln(µari/µgeo))^0,5

sd = e(2*ln(xari/xgeo))^0,5

scattering factor normal distribution sigma zeta phi deisenroth (streufaktornormalverteilung sigma zeta phi deisenroth)

σ(ϕ;n) = σ^±√(-ln(ϕ)/n) = σ^±ζ(ϕ;n) = x(ϕ;n)/µ

σ(ϕ;n) = σ^(±ζ(ϕ;n) = x(ϕ;n)/µ

ϕd(x;n) or ϕ(x;n) = e^(-n*((ln(x/µ))/(ln(σ))²)

x(ϕ;n) = µ∗σ^(±√((-ln(ϕ)/n)))

ϕ(σ;n) = e^(-n*((ln(x(ϕ;n)/µ))/(ln(σ))²)

ζ(ϕ;n) = ±√(-ln(ϕ)/n)

factor normal distribution (faktor normalverteilung = faktornormalverteilung = streufaktor normalverteilung = streufaktornormalverteilung)

probability limit factor normal distribution sigma zeta phi deisenroth = σd(ϕd;n) = σd^(±ζd(ϕd;n) = σd^±√(-ln(ϕd)/n) = x(ϕd;n)/µgeo ; σd=1,01

probability limit factor normal distribution sigma zeta phi deisenroth = σd(ϕd;n) = σd^(±ζd(ϕd)/n^0,5) = σd^(±√(-ln(ϕd)/n)) = x(ϕd;n)/µgeo ; σd=2