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

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

σ(ϕ;n) = σ^±√(-ln(ϕ)/n) = x(ϕ;n)/µ

standardstreufaktor sigma = σ

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

standard faktor sigma = σ

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

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;n)/µ

x(ϕ;n) = µ∗σ^±√(-ln(ϕ)/n)

x(phi,sigma,µ,n) deisenroth

x(ϕ;σ;µ;n) = µ∗σ^±√(-ln(ϕ)/n)

x(zeta,sigma,µ) deisenroth

x(ζ;σ;µ) = µ∗σ^±ζ

x(zeta,sigma,µ,n) deisenroth

x(ζ;σ;µ;n) = µ∗σ^(±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(σ)/√n = probability exponent zeta(phi) deisenroth

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

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

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

ζ(x/µ;σ;n) = ln(x/µ)/ln(σ)/√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) = ϕ(n)

ϕ(n) = ϕ^n

probability factor phi cum (n) = ϕc(n)

ϕc(n) = 0,5*ϕ^n

probability factor product phi cum product (n) = ϕcp(n)

ϕcp(n) = (0,5*ϕc)^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)

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

ϕ(n) = ϕ^(-1/n) = ϕ^n

estimated arithmetic mean (xari) and estimated geometric mean (xgeo)

xari = estimated arithmetic mean (geschätzter arithmetischer mittelwert)

xgeo = estimeted geometric mean (geschätzter geometrischer mittelwert)

xgeo(x_i;n) = e^(1/n*((ln(x₁)+ln(x₂)+.....+ln(x_n)))

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

xari(x_i;n) = 1/n*(x₁+x₂+ ....+x_n)

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)

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 distribution function sigma-cum(phi-cum) deisenroth = σc(ϕc;n;σd) = σd^(±√(-ln(2*ϕc)/n))

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

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

phi cumulative factor product distribution deisenroth = ϕ_cp;n = ϕcⁿ

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

Impressum

Frank Deisenroth

Seligenstädter Weg 4

63796 Kahl am Main

Tel.: 0179 / 110 3096

deisenroth@gmail.com

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