sigma zeta phi diagram deisenroth
= ϕ(ζ;n)
= e^-(ζ^2/n)
ζ = ±√(-ln(ϕ)/n) = ln(x/µ)/ln(σd)/√n

sigma zeta phi diagram deisenroth = ϕ(ζ;n) = e^-(ζ^2/n)

ζ = ±√(-ln(ϕ)/n) = ln(x/µ)/ln(σd)/√n

Impressum phi factor normal distribution ϕ(x/µ;σ;n) = e^(-n*(ln(x/µ)/ln(σ))²) 

probability factor phi(x/µ;sigma;n) deisenroth = ϕ(x/µ;σ;n)

ϕ(x/µ;σ;n) = e^(-n*(ln(x/µ)/ln(σ))²)

probability factor sigma(phi;n) deisenroth = σ(ϕ;n) 

σ(ϕ;n) = σd^±√(-ln(ϕ)/n) = x(ϕ;n)/µ

x(ϕ;n) = µ∗σd^±√(-ln(ϕ)/n)

x(phi,sigma,µ,n) deisenroth

x(ϕ;σd;µ;n) = µ∗σd^±√(-ln(ϕ)/n)

x(zeta,sigma,µ) deisenroth

x(ζ;σ;µ) = µ∗σd^±ζ

x(zeta,sigma,phi;µ) deisenroth

x(ζ;σd;ϕ;µ) = µ∗σd^±ζ(ϕ)

x(zeta,sigma,µ,n) deisenroth

x(ζ;σd;µ;n) = µ∗σd^(±ζ/√n)

probability exponent zeta deisenroth = ζ

ζ = ±√(-ln(ϕ)) = ln(x/µ)/ln(σ) 

probability exponent zeta(phi) deisenroth = ζ(ϕ) 

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

 probability exponent zeta(phi;n) deisenroth = ζ(ϕ;n) 

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

probability exponent zeta(x/µ;sigma) deisenroth = ζ(x/µ;σd)

ζ(x/µ;σd) = ln(x/µ)/ln(σd) = ±√(-ln(ϕ)) = probability exponent zeta(x/µ;sigma) deisenroth

probability exponent zeta(x/µ;sigma;n) deisenroth = ζ(x/µ;σd;n)

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

probability factor phi(zeta) deisenroth = ϕ(ζ) 

ϕ(ζ) = e^-(ζ^2) 

probability factor phi(zeta,n) deisenroth = ϕ(ζ;n) 

ϕ(ζ;n) = e^-(ζ^2/n) = e^-(ζ^2/n )

probability factor phi(n) deisenroth = ϕ(n)

ϕ(n) = ϕ^(-1/n) = ϕ^n 

sigma zeta phi diagram deisenroth = ϕ(ζ;n)=e^-(ζ^2/n)

ζ=±√(-ln(ϕ)/n)=ln(x/µ)/ln(σd)/√n

sigma zeta phi diagram deisenroth = ϕ(ζ;n)=e^-(ζ^2/n)

ζ=±√(-ln(ϕ)/n)=ln(x/µ)/ln(σd)/√n

sigma zeta phi diagram deisenroth = ϕ(ζ;n) =e^-(ζ^2/n)

 ζ = ±√(-ln(ϕ)/n)

sigma zeta phi diagram deisenroth = ϕ(ζ;n)=e^-(ζ^2/n); ζ=±√(-ln(ϕ)/n)=ln(x/µ)/ln(σ)/√n

sigma zeta phi diagram deisenroth = ϕ(ζ;n)=e^-(ζ^2/n); ζ=±√(-ln(ϕ)/n)=ln(x/µ)/ln(σ)/√n

sigma zeta phi diagram deisenroth = ϕ(ζ;n)=e^-(ζ^2/n); ζ=±√(-ln(ϕ)/n)=ln(x/µ)/ln(σ)/√n

sigma zeta phi diagram deisenroth = ϕ(ζ;n)=e^-(ζ^2/n); ζ=±√(-ln(ϕ)/n)=ln(x/µ)/ln(σ)/√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                  = 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^(±1/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

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

sdij = ? = estimated confidence limit factor sigma deisenroth ij

σdi(n,%) = σdi^(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(xgeoj/xgeoi)/(ln(σdi)/√ni + ln(σdj)/√nj) = true confidence limit exponent zeta deisenroth ij

Zdij=?= estimated confidence limit exponent zeta deisenroth ij

xgeoi = estimated geomean i

σdi = true standard scattering factor simga deisenroth i 

sdi = 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 = σdi^(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) = σdi^(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

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