porbability limit phi ϕd

probability limit phi deisenroth = ϕd

ϕd = e^(-n*(ln(x/µ)/ln(σ))²)

phi limit factor normal distribution deisenroth = ϕd(x/µ;σ;n) = e^(-n*(ln(x/µ)/ln(σ))²)

probability limit factor phi(x/µ;sigma;n) deisenroth = ϕd(x/µ;σ;n)

ϕd(x/µ;σ;n) = e^(-n*(ln(x/µ)/ln(σ))²)

probability limit factor sigma(phi;n) deisenroth = σ(ϕd;n)

σ(ϕd;n) = σ^±√(-ln(ϕ)/n) = x(ϕ)/µ

x(ϕd;n) = µ∗σ^±√(-ln(ϕ)/n)

probability limit factor phi(n) deisenroth = ϕd(n)

ϕd(n) = ϕd^n

standard limit factor sigma deisenroth σ and s (standardgrenzfaktor sigma deisenroth)

σ = e^(2*ln(µari/µgeo))^0,5 = true standard limit factor sigma (wahrer standardgrenzfaktor sigma deisenroth) = σd

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

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

µari = µgeo*e^(0,5*ln(σ)^2)

µgeo = µari/e^(0,5*ln(σ)^2)

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

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

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

xari(x_i;n) = 1/n*(x₁+x₂+ ....+x_n)

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

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

Frank Deisenroth

Seligenstädter Weg 4

63796 Kahl am Main

Tel.: 0179 / 110 3096

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