Scattering Factor Analysis

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

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

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

µari = true arithmetic mean (wahrer arithmetischer mittelwert)

µgeo = true geometric mean (wahrer geometrischer mittelwert)

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(sdi;n) = xari/e^(0,5*ln(sd)^2)

scattering probability limit factor normal distribution sigma zeta phi deisenroth

σd(ϕd;n) = σd^(±ζd(ϕd)/n^0,5) = 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) = ±√(-ln(ϕd))

probability limit base sigma deisenroth

σd(µari/µgeo) = e^(2∗ln(µari/µgeo))^0¸5

standard probability limit base sigma deisenroth

σd(µari/µgeo) = e^(2∗ln(µari/µgeo))^0¸5

standard probability limit factor sigma deisenroth

σd(µari/µgeo) = e^(2∗ln(µari/µgeo))^0¸5

standard probability limit exponent zeta deisenroth

ζd(ϕd=0,368) = 1

standard probability limit factor phi deisenroth

ϕd(ζd=1) = e^-ζd² = e^-1² = 0,368

standard sigma deisenroth

σd(µari/µgeo) = e^(2∗ln(µari/µgeo))^0¸5

standard zeta deisenroth

ζd(ϕd=0,368) = 1

standard phi deisenroth

ϕd(ζd=1) = e^-ζd² = e^-1² = 0,368

confidence limit base deisenroth

σd(µari/µgeo) = e^(2∗ln(µari/µgeo))^0¸5

confidence limit factor sigma deisenroth

σd(ϕd;n) = σd^(±ζd(ϕd)/n^0,5)

confidence limit exponent zeta deisenroth

ζd(ϕd) = ±√(-ln(ϕd))

confidence limit factor phi deisenroth

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

standard confidence limit factor sigma deisenroth

σd(µari/µgeo) = e^(2∗ln(µari/µgeo))^0¸5

standard confidence limit exponent zeta deisenroth

ζd(ϕd=0,368) = 1

standard confidence limit factor phi deisenroth

ϕd(ζd=1) = e^-ζd² = e^-1² = 0,368

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 *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 = true µgeo scattering factor (wahrer µgeo Streufaktor)

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

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

sd(n,%)=?=xgeo(n,%)/xgeo(100%)=estimated xgeo confidence limit factor sigma deisenroth (geschätz. Vertrauensgrenzfaktor)

sd(n,100%) = sd^±(ζd(100%)/n^0,5) = sd^(±0/n^0,5) = 1 = xgeo(n,100%)/xgeo(100%) = 1

sd(n,0%) = sd^±(ζd(0%)/n^0,5) = sd^±(∞/n^0,5) = ∞/1 and 1/∞ = ∞/xgeo(100%) and xgeo(100%)/∞=0

sd(n,100%) = 1

sd(n,0%) = 0 and ∞

σd(n,100%) = 1

σd(n,0%) = 0 and ∞

σd(n,36,8%) = σd^(1/n^0,5)

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

sd(n,%) =? (?= sd^(1/ζd(1-%)/(n)^0,5)=?) = xgeo(n,%,sd)/xgeo = estimated xgeo confidence limit factor deisenroth (gesch. VGF)

CLd(n,%,sd) =?=(?= sd^(1/ζd(1-%)^(2^0,5)/(n-2)^0,5)*xgeo) = estimated xgeo confidence limit deisenroth (geschätzte Vertrauensgrenze)

limit factor distirbution

probability limit base σd

probability limit factor ϕd

probability limit exponent ζd

probability limit factor σd(ϕd;n)

probability factor sigma deisenroth σd(ϕd;n)

probability factor phi deisenroth ϕd(xgeo;n)

probability exponent zeta deisenroth ζd

probability factor sigma deisenroth σd

probability limit base factor sigma deisenroth σd

standard probability limit factor sigma deisenroth σd

standard limit factor sigma deisenroth σd

confidence limit factor sigma deisenroth

confidence limit exponent zeta deisenroth

confidence limit base σd

scattering factor analysis deisenroth

probability phi 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

sdij = ? = estimated confidence limit factor sigma deisenroth ij

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

sdi(n,%) = ? = estimated 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

Zdij=?= estimated 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 = ? = 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) = ? = 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) = ? = xgeo(%;n)/µgeo = estimated xgeo probability limit factor sigma deisenroth

standard probability limit factor sigma deisenroth σd

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

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

Impressum

Frank Deisenroth

Seligenstädter Weg 4

63796 Kahl am Main

Tel.: 0179 / 110 3096

deisenroth@gmail.com

© Frank Deisenroth, Alle Rechte vorbehalten.