true arithmetic mean (µari) and true geometric mean (µgeo)
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 or µ = µari/e^(0,5*ln(σd)^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 factor sigma deisenroth σd and estimated standard scattering factor sigma deisenroth sd
σd = true standard scattering factor sigma deisenroth (wahrer 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)
phi factor normal distribution ϕ(x/µ;σd;n) = e^(-n*(ln(x/µ)/ln(σd))²) = phi faktor normalverteilung
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
sigma factor normal distribution σd(ϕ;n) = σd^(±√((-ln(ϕ)/n))) = x(ϕ;n)/µ = sigma faktor normalverteilung
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=2
µari = TRUE ARIMEAN (WAHRES ARIMITTEL)
µgeo = TRUE GEOMEAN (WAHRES GEOMITTEL)
σd = TRUE STANDARD SCATTERING FACTOR SIGMA DEISENROTH (WAHRER STANDARDSTREUFAKTOR)
sd = ESTIMATED STANDARD SCATTERING FACTOR SIGMA DEISENROTH (GESCHÄTZTER STANDARDSTREUFAKTOR)
xari = ESTIMATED ARIMEAN (GESCHÄTZTES ARIMITTEL)
xgeo = ESTIMATED GEOMEAN (GESCHÄTZTES GEOMITTEL)
σd (sd) = Standardstreufaktor sigma deisenroth
σd (sd) = standard scattering probability limit factor sigma deisenroth
factor normal distribution (Faktor Normalverteilung)
scattering factor analysis (Streufaktor Analyse)
Study scattering factor noise Deisenroth (Untersuchung Streufaktor Lärm Deisenroth)
Impressum
Frank Deisenroth
Seligenstädter Weg 4
63796 Kahl am Main
Tel.: 0179 / 110 3096
© Frank Deisenroth, Alle Rechte vorbehalten.