xgeo = estimated 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)

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

µari = µgeo*e^(0,5*ln(σd)^2)

µgeo = µari/e^(0,5*ln(σd)^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(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 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^(±√((-ln(ϕd)/n))) = x(ϕd;n)/µgeo

σd(ϕd;n) = σd^(±ζd(ϕd;n) = x(ϕd;n)/µgeo

ϕd(x;n) = e^(-n*((ln(x/µgeo))/(ln(σd))²)

x(ϕd;n) = µgeo∗σd^(±√((-ln(ϕd)/n)))

ϕd(σd;n) = e^(-n*((ln(x(ϕd;n)/µgeo))/(ln(σd))²)

ζd(ϕd) = ±√(-ln(ϕd)/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

Page updated

Google Sites

Report abuse