Probability Density Functions Used in the Calculation of Risk of Cancer Posed by Ingestion of Radon Gas in Water (following notation of EPA 1995)
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Variability
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Uncertainty
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Parameter
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Distribution Type
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Distribution Values
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Distribution Type
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Distribution Values
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C (concentration of radon in water, pCi/L[water])
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Lognormal distribution, LN(µ )
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C = LN(µ,σ) µ = TS(m,s,n) (σ)2=IChi(s,n)
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Student t, distribution, TS(m,s,n) Inverse chi-squared distribution, IChi(s,n)
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n= 10 m = ln(200) s = ln(1.85)
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V (volume of water ingested, L/d)
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Lognormal distribution, LN(µ,σ)
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V = LN(µ,σ) µ=TS(m,s,n) (σ)2=IChi(s,n)
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Student t distribution, TS(m,s,n) Inverse chi-squared distribution, IChi(s,n)
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n=100 m = ln(0.526) s = ln(1.922)
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F (fraction remaining)
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Beta distribution, B(m,md,min,max)
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F=B(m,md,min,max) min=0.5 max=1 m=U(a,b) md=U(m,max) or U(min,m)
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Uniform distributions U(a,b) U(m,max)
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a=0.7 b=0.9 min = 0.5 max=1
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RF (risk factor, cancer-death risk per person per pCi ingested)
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This factor has uncertainty only
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RF=LN(µ,σ)
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µ= ln(1.24 × 10-11 σ = ln(2.42)
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Calculated individual risk
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Uncertainty==> Variability 5th percentile mean 95th percentile
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5th percentile 1.7 × 10-8 1.3 × 10-7 4.0 × 10-7
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median 8.3 × 10-8 6.2 × 10-7 1.9 × 10-6
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95th percentile 3.4 × 10-7 2.6 × 10-6 7.9 × 10-6
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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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