cumulative probability limit factor product distribution function sigma-cum-product(phi-cum-product) deisenroth = σcp(ϕcp;n;σd) = σd^(±√(-ln(2^nϕcp)/n)) = σxgeosd = sigma(xgeosd) = xgeosd(ϕcp;n)= cumulativ confidence limit factor product deisenroth = x(ϕcp;n;σd)/µ= x(ϕ;n;σ)/µ or µ/x(ϕ;n;σ)

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(xgeo*sd) = xgeo*sd(ϕcp;n)= cumulative confidence limit factor product deisenroth = x(ϕcp;n;σd)/µ= x(ϕ;n;σ)/µ or µ/x(ϕ;n;σ)

cumulative probability limit factor product distribution function sigma-cum-product(phi-cum-product) deisenroth = σ_cp(ϕ_cp;n;σd) = σd^(±√(-ln(2^n*ϕ_cp)/n)) = σ_xgeo*sd = sigma(xgeo*sd) = xgeo*sd(ϕ_cp;n)= cumulative confidence limit factor product deisenroth = x(ϕ_cp;n;σd)/µ= x(ϕ;n;σ)/µ or µ/x(ϕ;n;σ); µ(ϕ_cp ;n;σd;xgeo) = xgeo*σd^(±√(-ln(2^n*ϕ_cp)/n))) = xgeo*σd^(±√(-ln(2^n*ϕ_cp)/n)); µ(ϕ;n;σ^±1;x_n)= x_n*σ^(±√(-ln(2^n*ϕ)/n)) = confidence interval deisenroth = µ(ϕ;n;σ^±1;x_n) ; σ^±1= true standard scattering probability limit normal factor deisenroth = e^(2*ln(µari/µ))^0,5= σ^±1; µari = true arithmetic mean; µ = true geometric mean; x_n=estimated geometric mean

example for phi-cum-product

ϕ_cp(x_n*sd<µ;n=1) < 0,5

ϕ_cp(x_n*sd<µ;n=2) < 0,25

ϕ_cp(x_n*sd<µ;n=3) < 0,125

ϕ_cp(x_n*sd<µ;n=4) < 0,0625

ϕ_cp(x_n*sd<µ;n=5) < 0,03125

ϕ_cp(x_n*sd<µ;n=6) < 0.015625

ϕ_cp(x_n*sd<µ;n=7) < 0.0078125 ≈ 1 percent (%) ≈ 1 error per hundert opportunities

ϕ_cp(x_n*sd<µ;n=8) < 0.00390625

ϕ_cp(x_n*sd<µ;n=9) < 0.001953125

ϕ_cp(x_n*sd<µ;n=10) < 0,00097 ≈ 10^-3 ≈ 1 promille (‰) ≈ 1 error per thousand opportunities

ϕ_cp(x_n*sd<µ;n=20) < 0,00000095 ≈ 10^-6 ≈ 1 ppm ≈ 1 error per million opportunities

ϕ_cp(x_n*sd<µ;n=30) < 9,31*10^-10 ≈ 10^-9 ≈ 1 ppb ≈ 1 error per billion opportunities

ϕ_cp(x_n*sd<µ;n=40) < 9,09*10^-13 ≈ 10^-12 ≈ 1 ppt ≈ 1 error per trillion opportunities