Table F.1

Probability Density Functions Used in the Calculation of Risk of Cancer Posed by Ingestion of Radon Gas in Water (following notation of EPA 1995)

 

Variability

Uncertainty

Parameter

Distribution Type

Distribution Values

Distribution Type

Distribution Values

C (concentration of radon in water, pCi/L[water])

Lognormal distribution, LN(µ)

C = LN(µ,σ) µ = TS(m,s,n) (σ)2=IChi(s,n)

Student t, distribution, TS(m,s,n) Inverse chi-squared distribution, IChi(s,n)

n= 10 m = ln(200) s = ln(1.85)

V (volume of water ingested, L/d)

Lognormal distribution, LN(µ,σ)

V = LN(µ,σ) µ=TS(m,s,n) (σ)2=IChi(s,n)

Student t distribution, TS(m,s,n) Inverse chi-squared distribution, IChi(s,n)

n=100 m = ln(0.526) s = ln(1.922)

F (fraction remaining)

Beta distribution, B(m,md,min,max)

F=B(m,md,min,max) min=0.5 max=1 m=U(a,b) md=U(m,max) or U(min,m)

Uniform distributions U(a,b) U(m,max)

a=0.7 b=0.9 min = 0.5 max=1

RF (risk factor, cancer-death risk per person per pCi ingested)

This factor has uncertainty only

 

RF=LN(µ,σ)

µ= ln(1.24 × 10-11σ = ln(2.42)

Calculated individual risk

Uncertainty==> Variability 5th percentile mean 95th percentile

5th percentile 1.7 × 10-8 1.3 × 10-7 4.0 × 10-7

median 8.3 × 10-8 6.2 × 10-7 1.9 × 10-6

95th percentile 3.4 × 10-7 2.6 × 10-6 7.9 × 10-6

m=mean value derived from a sample

s=standard deviation of a sample

n=sample size

md=mode of a sample

µ=mean value of ln(x) in a lognormal distribution

µ=standard deviation of ln(x) in a lognormal distribution



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