probability limit exponent zeta deisenroth ζ(ϕ;n) = ±√(-ln(ϕ)/n) = ln(x/µ)/ln(σ)/√n

probability limit factor normal distribution sigma zeta phi deisenroth

σ(ϕ;n) = σ^±ζ(ϕ;n) = σ^±√(-ln(ϕ)/n) = x(ϕ;n)/µ

ϕ(x;n) = e^(-n*((ln(x/µ))/(ln(σ))²)

ϕ(σ;n) = e^(-n*((ln(x(ϕ;n)/µ))/(ln(σ))²)

ζ(ϕ;n) = ±√(-ln(ϕ)/n)

probability limit factor sigma deisenroth

σ(ϕ;n) = σ^(±ζ(ϕ;n) = x(ϕ;n)/µ

probability limit factor phi deisenroth

ϕ(σ;n) = e^(-n*((ln(x(ϕ;n)/µ))/(ln(σ))²)

probability limit exponent zeta deisenroth

ζ(ϕ;n) = ±√(-ln(ϕ)/n)

probability limit factor sigma probability limit exponent zeta and probability limit factor phi diagram deisenroth

probability limit exponent zeta deisenroth

ζdi(ϕdi;ni) = ±√(-ln(ϕdij)/ni)= true probablitiy limit exponent zeta deisenroth

Zdi(Pdi;ni) = ±√(-ln(Pdi)/ni)= estimated probablitiy limit exponent zeta deisenroth

probability exponent zeta deisenroth

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

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

probability phi deisenroth

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

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

probability limit phi deisenroth

ϕdi(ζdi) = e^-(ζdi²) = true probability limit phi deisenroth

Pdi(Zdi;ni) = e^-(Zdi²/ni) = estimated probability limit phi deisenroth

probability limit factor sigma ij deisenroth

σdi(ϕdi;ni) = σd_i^√(-ln(ϕdi)/ni) = true probability limit factor sigma deisenroth i

probability limit exponent zeta ij deisenroth

ζdij = ln(xgeo_j/xgeo_i)/(ln(sd_i)/√n_i + ln(sd_j)/√n_j) = probability limit exponent zeta deisenroth

xgeo_i = estimated geomean i

sd_i = estimated standard scattering factor simga deisenroth i

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

scattering factor distribution

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

confidence limit exoponent zeta deisenroth ζd

probability phi deisenroth ϕd

scattering probability limit factor normal distribution sigma zeta phi deisenroth

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

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^±√(-ln(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)

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(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 =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)

confidence limit factor sigma xgeo = σxgeo(%;n) = Vertrauensgrenzfaktor xgeo

σxgeo(ϕd;n) = xgeo(ϕd;n)/µgeo = σd^-(((√-ln(ϕd))-2*ϕd)/n^0,5)

σxgeo(%;n) = xgeo(%;n)/µgeo = σd^-(((√-ln(%))-2*%)/n^0,5)

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)

probability limit exponent zeta deisenroth

ζdi(ϕdi;ni) = ±√(-ln(ϕdij)/ni)= true probablitiy limit exponent zeta deisenroth

Zdi(Pdi;ni) = ±√(-ln(Pdi)/ni)= estimated probablitiy limit exponent zeta deisenroth

probability exponent zeta deisenroth

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

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

probability phi deisenroth

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

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

probability limit phi deisenroth

ϕdi(ζdi) = e^-(ζdi²) = true probability limit phi deisenroth

Pdi(Zdi) = e^-(Zdi²) = estimated probability limit phi deisenroth

Confidence limit factor sigma deisenroth

σdi(ϕdi;ni) = σd_i^√(-ln(ϕdi)/ni) = true confidence limit factor sigma deisenroth i

sdi(Pdi;ni) = sd_i^(√(-ln(Pdij)/ni) = estimated confidence limit factor sigma deisenroth ij

σdi(ni,%) = σd_i^(√(-ln(%)/ni) = true confidence limit factor sigma deisenroth i

sdi(ni,%) = sd_i^(√(-ln(%)/ni)) = 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

Zdij=(ln(xgeo_j/xgeo_i)/(ln(sd_i)/√(n_i -2)+ln(sd_j)/√(n_j-2))^(1/2^0,5) = estimated confidence limit exponent zeta deisenroth

xgeo_i = estimated geomean i

σd_i = true standard scattering factor simga deisenroth i

sd_i = estimated standard scattering factor simga deisenroth i

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

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