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x µ σ standard normal factor simulation
probability factor normal distribution sigma zeta phi deisenroth = σ(ϕ;n) = σ^±ζ(ϕ;n) = σ^±√(-ln(ϕ)/n) = x(ϕ;n)/µ
probability factor normal distribution sigma zeta phi deisenroth = σ(ϕ;n) = σ^±ζ(ϕ;n) = σ^±√(-ln(ϕ)/n) = x(ϕ;n)/µ
σ = e^(2∗ln(µari/µgeo))^0¸5 = true standard normal factor sigma deisenroth (wahrer Standardnormalfaktor sigma deisenroth)
sd = e^(2∗ln(xari/xgeo))^0¸5 = estimated standard normal factor sigma deisenroth (geschätzter Standardnormalfaktor sigma deisenroth)
true arithmetic mean (µari) and true geometric mean (µgeo or µ)
µari = true arithmetic mean (wahrer arithmetischer mittelwert)
µgeo = true geometric mean (wahrer geometrischer mittelwert)
µari = µ*e^(0,5*ln(σ)^2)
µ = µari/e^(0,5*ln(σ)^2)
estimated arithmetic mean (xari) and estimated geometric mean (xgeo)
xari = estimated arithmetic mean (geschätzter arithmetischer mittelwert)
xgeo = estimeted geometric mean (geschätzter geometrischer mittelwert)
xgeo(xi;n) = e^(1/n*((ln(x1)+ln(x2)+.....+ln(xn)))
xgeo(sd;xari) = xari/e^(0,5*ln(sd)^2)
xari(xi;n) = 1/n*(x1+x2+ ....+xn)
xari(sd;xgeo) = xgeo*e^(0,5*ln(sd)^2)
true standard scattering probability limit factor sigma deisenroth σd and estimated standard scattering probability limit factor sigma deisenroth sd
σd = e^(2*ln(µari/µgeo))^0,5
sd = e^(2*ln(xari/xgeo))^0,5
scattering probability limit factor normal distribution sigma zeta phi deisenroth
σd(ϕd;n) = σd^(±ζd(ϕd;n) = x(ϕd;n)/µgeo
ϕd(x;n) = e^(-n*((ln(x/µgeo))/(ln(σd))²)
ϕd(σd;n) = e^(-n*((ln(x(ϕd;n)/µgeo))/(ln(σd))²)
ζd(ϕd;n) = ±√(-ln(ϕd)/n)
limit factor sigma deisenroth
σd(ϕd;n) = σd^(±ζd(ϕd;n) = x(ϕd;n)/µgeo
limit factor phi deisenroth
ϕd(σd;n) = e^(-n*((ln(x(ϕd;n)/µgeo))/(ln(σd))²)
limit exponent zeta deisenroth
ζd(ϕd;n) = ±√(-ln(ϕd)/n)
scattering probability limit factor normal distribution sigma zeta phi deisenroth
σ(ϕ;n) = σ^(±ζ(ϕ;n) = x(ϕ;n)/µ
ϕ(x;n) = e^(-n*((ln(x/µ))/(ln(σ))²)
ϕ(σ;n) = e^(-n*((ln(x(ϕ;n)/µ))/(ln(σ))²)
ζ(ϕ;n) = ±√(-ln(ϕ)/n)
probability limit base sigma deisenroth
σd(µari/µgeo) = e^(2∗ln(µari/µgeo))^0¸5
standard probability limit base sigma deisenroth
σd(µari/µgeo) = e^(2∗ln(µari/µgeo))^0¸5
standard probability limit factor sigma deisenroth
σd(µari/µgeo) = e^(2∗ln(µari/µgeo))^0¸5
standard probability limit exponent zeta deisenroth
ζd(ϕd=0,368) = 1
standard probability limit factor phi deisenroth
ϕd(ζd=1) = e^-ζd² = e^-1² = 0,368
standard sigma deisenroth
σd(µari/µgeo) = e^(2∗ln(µari/µgeo))^0¸5
standard zeta deisenroth
ζd(ϕd=0,368) = 1
standard phi deisenroth
ϕd(ζd=1) = e^-ζd² = e^-1² = 0,368
confidence limit base deisenroth
σd(µari/µgeo) = e^(2∗ln(µari/µgeo))^0¸5
confidence limit factor sigma deisenroth
σd(ϕd;n) = σd^(±ζd(ϕd;n)
confidence limit exponent zeta deisenroth
ζd(ϕd) = ±√(-ln(ϕd)/n)
confidence limit factor phi deisenroth
ϕd(σd;n) = e^(-n*((ln(x(ϕd;n)/µgeo))/(ln(σd))²)
standard confidence limit factor sigma deisenroth
σd(µari/µgeo) = e^(2∗ln(µari/µgeo))^0¸5
standard confidence limit exponent zeta deisenroth
ζd(ϕd=0,368) = 1
standard confidence limit factor phi deisenroth
ϕd(ζd=1) = e^-ζd² = e^-1² = 0,368
Frank Deisenroth
Seligenstädter Weg 4
63796 Kahl am Main
Tel.: 0179 / 110 3096
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