standard limit factor sigma deisenroth σd

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

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

µari = TRUE ARIMEAN 

µgeo = TRUE GEOMEAN

xari = ESTIMATED ARIMEAN 

xgeo = ESTIMATED GEOMEAN 

xari(xi) = 1/n*(x1+x2+ ....+xn)

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

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) 

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

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

scattering factors (Streufaktoren) 

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

sd = e^(2∗ln(xari/xgeo))^0¸5            = estimated standard scattering 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(ϕd;n)*x/µgeo                              = true scattering factor product (wahres Streufaktorprodukt)

sp =   sd*xgeo/µgeo                               = 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(100%)           = true µgeo scattering factor (wahrer µgeo Streufaktor)

σxgeo(n,%) = xgeo(n,%)/xgeo(100%)           = true xgeo scattering factor (wahrer xgeo Streufaktor)

σd(n,%) =x(n,%)/µgeo = true x confidence limit factor sigma deisenroth (wahrer Vertrauensgrenzfaktor)

σd(n,%) =µgeo(n,%)/µgeo

CLd(n,%,σd)  = true x confidence limit deisenroth (wahre x Vertrauensgrenze)

 sd(n,%)                                                     = xgeo(n,%,sd)/xgeo = estimated xgeo confidence limit factor deisenroth (gesch. VGF)

CLd(n,%,sd)                                              = estimated xgeo confidence limit deisenroth (geschätzte Vertrauensgrenze)

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)

Confidence limit factor sigma deisenroth

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

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

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

confidence limit exponent zeta deisenroth

ζdij = ln(xgeoj/xgeoi)/(ln(σdi)/√ni + ln(σdj)/√nj) = true confidence limit exponent zeta deisenroth

xgeoi = estimated geomean i

σdi = true standard scattering factor simga deisenroth i 

probability phi deisenroth

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

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

probability limit phi deisenroth

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

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

probability exponent zeta deisenroth

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

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

Impressum

Frank Deisenroth

Seligenstädter Weg 4

63796 Kahl am Main

Tel.: 0179 / 110 3096

deisenroth@gmail.com

© Frank Deisenroth, Alle Rechte vorbehalten.