zeta sigma diagram deisenroth σ(ζ) = σ^(±ζ(ϕ;n) = σ^±√(-ln(ϕd)/n) = x(ϕ;n)/µ

zeta sigma diagram deisenroth σ(ζ) = σ^(±ζ(ϕ;n) = σ^±√(-ln(ϕd)/n) = x(ϕ;n)/µ

probability factor phi deisenroth

probability factor sigma deisenroth

probability limit factor normal distribution sigma zeta phi deisenroth

scattering probability limit factor normal distribution sigma zeta phi deisenroth

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

σd(ϕd;n) = σd^(±√((-ln(ϕd)/n))) = x(ϕd;n)/µgeo

x(ϕd;n) = µgeo∗σd^(±√((-ln(ϕd)/n)))

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

ϕd(σd;n) = e^(-n*((ln(xgeo(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

σd(ϕd;n) = σd^(±√((-ln(ϕd)/n))) = x(ϕd;n)/µgeo

x(ϕd;n) = µgeo∗σd^(±√((-ln(ϕd)/n)))

limit factor phi deisenroth

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

limit exponent zeta deisenroth

ζd(ϕd) = ±√(-ln(ϕd)/n)

scattering factors (Streufaktoren)

σd = e^(2∗ln(µari/µgeo))^0¸5 = true standard scattering probability limit factor sigma deisenroth (wahrer Standardstreufaktor)

sd = e^(2∗ln(xari/xgeo))^0¸5 = estimated standard scattering probability limit factor sigma deisenroth (geschätzter Standardstreufaktor)

σari = µari/µgeo = e^(0,5∗(ln σd)^² ) = true µari scattering factor (wahrer Aristreufaktor)

sari = xari/xgeo = e^(0,5∗(ln sd)^²) = estimated xari scattering factor (geschätzter Aristreufaktor)

σp = σd *σari = true scattering factor product (wahres Streufaktorprodukt)

sp = sd * sari = estimated scattering factor product (geschätztes Streufaktorprodukt)

σgeo = µgeo/µgeo = 1 = true µgeo scattering factor (wahrer µgeo Streufaktor)

sgeo = xgeo/xgeo = 1 = estimated xgeo scattering factor (geschätzter xgeo Streufaktor)

σxgeo = xgeo/µgeo = true xgeo scattering factor (wahrer xgeo Streufaktor)

σµgeo(n,%) = µgeo(n,%)/µgeo(50%) = true µgeo scattering factor (wahrer µgeo Streufaktor)

σxgeo(n,%) = xgeo(n,%)/xgeo(50%) = true xgeo scattering factor (wahrer xgeo Streufaktor)

σd(n,%) =xgeo(n,%)/µgeo =σd^(Z(%)/n^0,5)= true xgeo confidence limit factor sigma deisenroth (wahrer Vertrauensgrenzfaktor)

σd(n,%) =µgeo(n,%)/µgeo =σd^(Z(%)/n^0,5)= true µgeo confidence limit factor sigma deisenroth (wahrer Vertrauensgrenzfaktor)

CLd(n,%,σd) = σd^(Z(%)/n^0,5) * xgeo = true xgeo confidence limit deisenroth (wahre xgeo Vertrauensgrenze)

probability factor sigma deisenroth σd(ϕd;n)

standard limit factor sigma deisenroth

confidence limit factor sigma deisenroth

confidence limit exponent zeta deisenroth

probaility limit phi deisenroth

probability limit exponent zeta deisenroth

scattering factor analysis deisenroth

scattering factor limit analysis deisenroth

µari = TRUE ARIMEAN (WAHRES ARIMITTEL)

µgeo = TRUE GEOMEAN (WAHRES GEOMITTEL)

xari = ESTIMATED ARIMEAN (GESCHÄTZES ARIMITTEL)

xgeo = ESTIMATED GEOMEAN (GESCHÄTZTES GEOMITTEL)

xgeo(xi) = e^(1/n*((ln(x1)+ln(x2)+.....+ln(xn)))

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

σd (sd) = standard scattering factor sigma Deisenroth

σd (sd) = Standardstreufaktor sigma Deisenroth

σd =TRUE SCATTERING FACTOR SIGMA DEISENROTH (WAHRER STANDARDSTREUFAKTOR DEISENROTH)

sd =ESTIMATED SCATTERING FACTOR SIGMA DEISENROTH (GSCHÄTZTER STANDARDSTREUFAKTOR DEISENROTH)

scattering factor analysis (Streufaktoranalyse)

Study scattering factor noise Deisenroth (Untersuchung Streufaktor Lärm Deisenroth)

σd (sd) = standard probability factor sigma Deisenroth

σd (sd) = Standard - Wahrscheinlichkeitsfaktor sigma Deisenroth

σd =TRUE STANDARD PROBABILITY FACTOR SIGMA DEISENROTH (WAHRER STANDARD WAHRSCHEINLICHKEITSFAKTOR SIGMA DEISENROTH)

sd =ESTIMATED STANDARD PROBABILITY FACTOR SIGMA DEISENROTH (GSCHÄTZTER WAHRSCHEINLICHKEITSFAKTOR DEISENROTH)

scattering factor analysis (Wahrscheinlichkeitsfaktor - Analyse)

Confidence limit factor sigma deisenroth

σdij = σd_i^(ζdij/ni^0,5) = true confidence limit factor sigma deisenroth ij

σdi(n,%) = σd_i^(ζd/ni^0,5) = true confidence limit factor sigma deisenroth i

confidence limit exponent zeta deisenroth

ζdij = ln(xgeo_j/xgeo_i)/(ln(σd_i)/√n_i + ln(σd_j)/√n_j) = true confidence limit exponent zeta deisenroth ij

xgeo_i = estimated geomean i

σd_i = true standard scattering factor simga deisenroth i

sd_i = estimated standard scattering factor simga deisenroth i

probability phi deisenroth ϕd(ζd)

ϕd(ζd) = e^-ζd² = true probability phi deisenroth

Pd(Zd) = e^-Zd² = estimated probability phi deisenroth

probability limit phi deisenroth ϕdij(ζdij)

ϕdij(ζdij) = e^-ζdij² = true probability limit phi deisenroth

Pdij(Zdij) = e^-Zdij² = estimated probability limit phi deisenroth

probability exponent zeta deisenroth ζd(ϕd)

ζd(ϕd) = ±√(-ln(ϕd)) = true probablitiy exponent zeta deisenroth

Zd(Pd) = ±√(-ln(Pd))= estimated probablitiy exponent zeta deisenroth

probability limit exponent zeta deisenroth ζdij(ϕdij)

ζdij(ϕdij) = ±√(-ln(ϕdij))= true probablitiy limit exponent zeta deisenroth ij

Zdij(Pdij) = ±√(-ln(Pdij))= estimated probablitiy limit exponent zeta deisenroth ij

probability limit factor sigma deisenroth σdij

σdij = σd_i^(ζdij/ni^0,5) = true probability limit factor sigma deisenroth ij

sdij = sd_i^(Zdij^(2^0,5)/(ni-2)^0,5) = estimated probability limit factor sigma deisenroth ij

probability limit factor sigma deisenroth σdi(ζdi;ni)

σdi(ζdi;ni) = σd_i^(ζdi/ni^0,5) = true probability limit factor sigma deisenroth i

sdi(Zdi,ni) = sd_i^(Zdi^(2^0,5)/((ni-2)^0,5) = estimated probability limit factor sigma deisenroth i

probability limit factor sigma deisenroth σd(%;n)

σd(%;n) = σd^(ζd(%)/n^0,5) = xgeo(%;n)/µgeo = true xgeo probability limit factor sigma deisenroth

sd(%;n) = sd^(Zd(%)^(2^0,5)/((ni-2)^0,5) = xgeo(%;n)/µgeo = estimated xgeo probability limit factor sigma deisenroth

Impressum

Frank Deisenroth

Seligenstädter Weg 4

63796 Kahl am Main

Tel.: 0179 / 110 3096

deisenroth@gmail.com

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