streufaktor = x/µ = σ(x/µ) = σ(ϕ) = phi limit factor sigma deisenroth
streufaktor sigma(phi) = σ(ϕ) = σd^±ϕ = x(ϕ)/µ
σd^±1 = streufaktorintervall = sigma faktor intervall = sigma intervall = sigmaintervall
= sigma faktorintervall = sigma factor interval deisenroth = σd^±1
wahrscheinlichkeitsdichte phi'(x,n=1) = ϕ'(x;n=1) = konstant für alle x/µ im Intervall σd^-1 und σd^+1

streufaktor sigma(phi) = σ(ϕ) = σd^±ϕ = x(ϕ)/µ

streufaktorprodukt sigma(phi;n) = σ(ϕ;n) = σd^±√(-ln(ϕ)/n) = x(ϕ;n)/µ = phi limit factor product sigma deisenroth
umkehrfunktion = inverse function =
wahrscheinlichkeitsfaktorprodukt phi(x;n) = ϕ(x/µ;σd;n) = e^(-n(ln(x/µ)/ln(σd))²)
= ϕ(σ;n) = phi (sigma) faktor normalverteilung = phi (sigma) factor normal distribution
= probability factor normal distribution deisenroth
= faktor normalverteilung für stichproben aus dem sigmafaktorintervall σd^±1
= faktor normalverteilung für stichproben aus der streufaktorprodukt normalverteilung σcp(ϕ=2/3)
&
ϕ'(x/µ;n) = scattering factor product probability density normal distribution phi'(x/µ)
= streufaktorprodukt wahrscheinlichkeitsdichte normalverteilung
ϕ'(x/µ;n) = abs(2ne^(-n(ln(x/µ)/ln(σd))²)ln(x)/((ln(σd))^2/x)
&
σ(ϕ;n) = σd^±√(-ln(ϕ)/n) = x(ϕ;n)/µ
= sigma(phi) faktor normalverteilung = sigma(phi) factor normal distribution
= streufaktornormalverteilung deisenroth = scattering factor normal distribution deisenroth
&
σd = e^(2ln(µari/µgeo))^0,5 = wahrer standardstreufaktor sigma deisenroth
= wahrer standardfaktor deisenroth
= true standard scattering factor sigma deisenroth
= true standard phi limit factor sigma deisenroth
&
σcp = e^(2ln(xari/xgeo))^0,5
= geschätzter standardstreufaktor sigma deisenroth
= estimated standard scattering factor sigma deisenroth
= estimated standard phi limit factor sigma deisenroth
&
µari = wahrer arithmetischer mittelwert = true arithmetic mean
µgeo = wahrer geometrischer mittelwert = true geometric mean
&
xari = geschätzter arithmetischer mittelwert = estimated arithmetic mean
xgeo = geschätzter geometrischer mittelwert = estimated geometric mean

streufaktorprodukt sigma(phi;n) = σ(ϕ;n) = σd^±√(-ln(ϕ)/n) = x(ϕ;n)/µ

streufaktor normalverteilung ϕ(x/µ) = phi(x/µ) deisenroth und simulation kumulatives wahrscheinlichkeitsprodukt ϕcp(x1*x2) und streufaktorprodukt σcp(ϕcp)

phi kumulativprodukt normalverteilung = ϕcp(xgeo/µgeo*sd^+1 > 1) = ϕ(σcp)^n = (2/3)^n = phi cumulative product normal distribution

probability factor phi(x) = ϕ(x) and probability density phi'(x) = ϕ'(x) and cumulative probability factor phi cum (x) = ϕc(x) normal distribution deisenroth; x µ σ standard factor simulation

streufaktor normalverteilung sigma(phi) = σ(ϕ) = σ^±√(-ln(ϕ)) = x(ϕ)/µ & wahrscheinlichkeitsfaktor normalverteilung phi(x) = ϕ(x/µ;σ;n) = e^(-n*(ln(x/µ)/ln(σ))²) analyse & monte carlo simulation kumulative wahrscheinlichkeit ϕc(x) = 0,5*ϕ(x) & wahrer standard streufaktor σ = e^(2∗ln(µari/µgeo))^0¸5 = e^(2∗ln(µari/µ))^0¸5 & geschätzter standard streufaktor sd = e^(2∗ln(xari/xgeo))^0¸5 & phi faktor normalverteilung deisenroth

unterseiten:

faktor normalverteilung ϕ(x) = phi(x) deisenroth

wahrscheinlichkeitsfaktor normalverteilung sigma zeta phi deisenroth ϕ(x/µ) = e^(-n*((ln(x/µ))/(ln (σ))²)

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

x(ϕ;n) = µ∗σ^±√(-ln(ϕ)/n) = phi faktor normalverteilung = wahrscheinlichkeitsfaktor normalverteilung = x(phi)

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

streufaktorprodukt

phi cumulative factor product distribution function deisenroth = ϕcp;n = ϕc^n and standard factor simulation xgeo*sd^+1 and xgeo*sd^-1

project definition phi'(x/µ) = ϕ'(x/µ) = ?

wahrscheinlichkeitsdichte normalverteilung funktion deisenroth = phi'(x) = ϕ'(x) = abs(2n*e^(-n*(ln(x/µ)/ln(σ))²)*ln(x)/((ln(σ))^2/x)

probability density normal distribution function deisenroth phi'(x) = ϕ'(x) = abs(2n*e^(-n*(ln(x/µ)/ln(σ))²)*ln(x)/((ln(σ))^2/x)

wahrscheinlichkeitsprodukt normalverteilung ϕcp(x/µ;n) = ϕc(x/µ)^n = (0,5*ϕ(x/µ))^n = phi cum product = phi kumulativ produkt = wahrscheinlichkeitsfaktorprodukt

standardabweichung normalverteilung deisenroth ϕ(x-µ) ≈ 0,5*e^(-n/2*((x-µ)/(ln(σ))²) und wahrscheinlichkeitsfaktor normalverteilung deisenroth ϕ(x/µ) = e^(-n*((ln(x/µ))/(ln (σ))²)

standardstreufaktor sigma deisenroth σ = σd

(= standardfaktor = grenzfaktor = standardgrenzfaktor = normalfaktor = standardnormalfaktor = standardnormalgrenzfaktor)

σ = σd = e^(2*ln(µari/µgeo))^0,5 = wahrer standardstreufaktor sigma deisenroth

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

µari = true arithmetic mean (wahrer arithmetischer mittelwert)

µgeo = true geometric mean (wahrer geometrischer mittelwert)

µari = µgeo*e^(0,5*ln(σd)^2)

µgeo = µari/e^(0,5*ln(σd)^2) ≠ µari for phi factor and phi density normal distribution

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

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

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

true standard scattering probability limit factor sigma deisenroth σd and estimated standard scattering probability limit factor sigma deisenroth sd

σd = true standard scattering probability limit factor sigma deisenroth (wahrer standardstreufaktor deisenroth)

sd = estimated standard scattering probability limit factor sigma deisenroth (geschätzter standardstreufaktor deisenroth)

σd = e(2*ln(µari/µgeo))^0,5 = wahrer standardstreufaktor sigma deisenroth = σ

sd = e(2*ln(xari/xgeo))^0,5 = geschätzter standardstreufaktor sigma deisenroth = s

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

probability factor function normal distribution sigma zeta phi deisenroth = σd(ϕd;n) = σd^±ζd(ϕd;n) = σd^±√(-ln(ϕd/n) = x(ϕd;n)/µgeo ; σd=1,01 and cumulative factor function deisenroth

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 and monte carlo simulation xgeo(n=1)

probability limit factor normal distribution sigma zeta phi deisenroth = σd(ϕd;n) = σd^(±ζd(ϕd)/n^0,5) = σd^(±√(-ln(ϕd))) = x(ϕd;n)/µgeo ; σd=1,01

probability limit factor normal distribution sigma zeta phi deisenroth = σd(ϕd;n) = σd^(±ζd(ϕd)/n^0,5) = σd^(±√(-ln(ϕd))) = x(ϕd;n)/µgeo ; σd=2

probability limit factor normal distribution sigma zeta phi deisenroth = σd(ϕd;n) = σd^(±ζd(ϕd)/n^0,5) = σd^(±√(-ln(ϕd))) = x(ϕd;n)/µgeo ; σd=1,01 and monte carlo simulation n=56

probability limit factor normal distribution sigma zeta phi deisenroth = σd(ϕd;n) = σd^(±ζd(ϕd)/n^0,5) = σd^(±√(-ln(ϕd))) = x(ϕd;n)/µgeo ; σd=2 and monte carlo simulation n=56

probability limit factor normal distribution sigma zeta phi deisenroth = σd(ϕd;n) = σd^(±ζd(ϕd)/n^0,5) = σd^(±√(-ln(ϕd))) = x(ϕd;n)/µgeo ; σd=1,01 and monte carlo simulation xgeo(n=2)

probability factor function sigma zeta phi deisenroth

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

x(ϕd;n) = µgeo ∗ σd^(±√((-ln(ϕd)/n)))

standard scattering factor (Standard Streufaktor)

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

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

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

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

σ(ϕ) = σ^±√(-ln(ϕ)) = x(ϕ)/µ = sigma(phi)

σc(ϕ) = σ^±√(-ln(2*ϕ)) = x(ϕc)/µ = kumulativer streufaktor = cumulative scattering factor = sigma cum

σcp(n) = (x1/µ*x2/µ...*xn/µ) = σ(x1/µ)*σ(x2/µ)...= x1/µ*x2/µ^2=xgeo^2/µ^2 = σcp(n) kumulativ streufaktorprodukt = σcp(n) = cumulative scattering factor product = sigma cum product

σcp(n)^(1/n) = σcp(xgeo/µ) = xgeo/µ = xgeo streufaktorprodukt = xgeo scattering factor product

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)

wahrscheinlichkeit phi, phi cum; phi cum product

ϕ = phi = wahrscheinlichkeit = probability

ϕc = phi cum = kumulativ wahrscheinlichkeit = cumulative probability

ϕcp = phi cum product = kumulativ wahrscheinlichkeit produkt = wahrscheinlichkeitsprodukt = phi cumulative product

vertrauensgrenzfaktor sigma(phi;n) deisenroth = σ(ϕ;n)

σ(ϕ;n) = σ^±√(-ln(ϕ)/n) = xgeo(ϕ;n)/µ

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 der Streufaktoren von DIN 45645, DIN EN ISO 9612 und TRLV-Lärm)

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

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 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) = 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 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) = σ^±√(-ln(ϕ)/n) = x(ϕ)/µ

x(ϕ;n) = µ∗σ^±√(-ln(ϕ)/n)

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

ϕ(n) = ϕ^n

standard factor sigma deisenroth σ and s (standardfaktor sigma deisenroth)

σ = e^(2*ln(µari/µgeo))^0,5 = true standard factor sigma (wahrer standardfaktor sigma deisenroth) = σd

s = e^(2*ln(xari/xgeo))^0,5 = estimated standard factor sigma (geschätzter standardfaktor sigma deisenroth) = sd

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

µari = true arithmetic mean (wahrer arithmetischer mittelwert)

µgeo = true geometric mean (wahrer geometrischer mittelwert)

µari = µgeo*e^(0,5*ln(σ)^2)

µgeo = µari/e^(0,5*ln(σ)^2)

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(s;xari) = xari/e^(0,5*ln(s)^2)

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

xari(s;xgeo) = xgeo*e^(0,5*ln(s)^2)

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

phi faktor normalverteilung ϕd(x/µ;σd;n) = e^(-n*(ln(x/µ)/ln(σd))²)

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

phi factor normal distribution ϕd(x/µ;σd;n) = e^(-n*(ln(x/µ)/ln(σd))²)

phi cumulative factor distribution function = ϕc = 0,5*ϕd(x/µ;σd;n)

cumulative probability limit factor distribution function phi-cum deisenroth = ϕc(x/µ;σd;n ) = 1/2*ϕd(x/µ;σc;n) and sigma-cum deisenroth = σc(ϕc;n) = σd^(±√(-ln(2*ϕc)/n))

cumulative probability limit factor product distribution function sigma-cum-product(phi-cum-product) deisenroth = σcp(ϕcp;n;σd) = σd^(±√(-ln(2^n*ϕcp)/n)) = σxgeo*sd

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

Impressum

Frank Deisenroth

Seligenstädter Weg 4

63796 Kahl am Main

Tel.: 0179 / 110 3096

deisenroth@gmail.com