standard factor sigma = σ = e^(2∗ln(µari/µ))^0¸5

standard factor sigma = σ

σ = e^(2∗ln(µari/µgeo))^0¸5

sd = e^(2∗ln(xari/xgeo))^0¸5

σ = TRUE STANDARD FACTOR SIGMA DEISENROTH (WAHRER STANDARDFAKTOR SIGMA DEISENROTH)

sd = ESTIMATED STANDARD FACTOR SIGMA DEISENROTH (GSCHÄTZTER STANDARDFAKTOR 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(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(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)

standard factor sigma = σ = e^(2∗ln(µari/µ))^0¸5

standard factor sigma = σ = e^(2∗ln(µari/µ))^0¸5

standard factor sigma = σ = e^(2∗ln(µari/µ))^0¸5

standard factor sigma = σ = e^(2∗ln(µari/µ))^0¸5

standard factor sigma = σ = e^(2∗ln(µari/µ))^0¸5

standard factor sigma = σ = e^(2∗ln(µari/µ))^0¸5

standard factor sigma = σ = e^(2∗ln(µari/µ))^0¸5

standard factor sigma = σ = e^(2∗ln(µari/µ))^0¸5

standard factor distribution

ϕ(x;n) = e^(-n*((ln(x/µ))/(ln(σ))²)

standar factors (Standardfaktoren)

σ = e^(2∗ln(µari/µgeo))^0¸5 = true standard factor sigma deisenroth (wahrer Standardfaktor)

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

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;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,phi;µ) deisenroth

x(ζ;σ;ϕ;µ) = µ∗σ^±ζ(ϕ)

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;n) 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) deisenroth = ϕ(n)

ϕ(n) = ϕ^(-1/n) = ϕ^n

Impressum

Frank Deisenroth

Seligenstädter Weg 4

63796 Kahl am Main

Tel.: 0179 / 110 3096

deisenroth@gmail.com

© Frank Deisenroth, Alle Rechte vorbehalten.