confidence limit base σd

confidence limit base σd (or σ)

true confidence limit base sigma deisenroth σd(µari/µari) (or σd(µari/µ) )

σd(µari/µgeo) = e^(2∗ln(µari/µgeo))^0¸5  =  true confidence limit base sigma deisenroth (wahre Vertrauensgrenzbasis) = σd 

estimated confidence limit base sigma deisenroth sd(xari/xgeo) 

sd(xari/xgeo) = e^(2∗ln(xari/xgeo))^0¸5   = estimated confidence limit base sigma deisenroth (geschätzte Vertrauensgrenze- Basis) = sd

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

µari = true arithmetic mean (wahrer arithmetischer mittelwert)

µgeo or µ = true geometric mean (wahrer geometrischer mittelwert) 

µari = µgeo*e^(0,5*ln(σd)^2)

µgeo = µari/e^(0,5*ln(σd)^2) = µ

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 = true standard scattering probability limit factor sigma deisenroth (wahrer standardfaktor deisenroth) = σ 

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

σd = e(2*ln(µari/µgeo))^0,5 = σ

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

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