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	PROBABILITY DISTRIBUTIONS
	Distribution Definitions & Parameter Reference
	DISTRIBUTION TYPE REFERENCE
	Distribution	Formula	Parameters	Mean	Variance	Best Use Case	Skewness	PDF Shape	Excel Function
	Normal	f(x) = (1/σ√2π)e^(-(x-μ)^2/2σ^2)	μ (mean), σ (std dev)	μ	σ^2	Revenue growth, price changes	0 (Symmetric)	Bell curve	NORM.INV(RAND(),μ,σ)
	Lognormal	f(x) = (1/xσ√2π)e^(-(ln(x)-μ)^2/2σ^2)	μ (log mean), σ (log std)	e^(μ+σ^2/2)	(e^(σ^2)-1)e^(2μ+σ^2)	Asset prices, market cap	Right-skewed (>0)	Right-tailed	LOGNORM.INV(RAND(),μ,σ)
	Triangular	Piecewise linear	a (min), b (mode), c (max)	(a+b+c)/3	(a^2+b^2+c^2-ab-ac-bc)/18	Cost estimates, project durations	Depends on a,b,c	Triangle	Custom (see engine)
	Uniform	f(x) = 1/(b-a)	a (min), b (max)	(a+b)/2	(b-a)^2/12	Unknown dist, equal likelihood	0 (Symmetric)	Rectangle	a+RAND()*(b-a)
	Beta	f(x) = x^(α-1)(1-x)^(β-1)/B(α,β)	α (shape1), β (shape2)	α/(α+β)	αβ/((α+β)^2(α+β+1))	Percentages, probabilities, rates	Depends on α,β	Flexible	BETA.INV(RAND(),α,β)
	VARIABLE DISTRIBUTION ASSIGNMENTS
	Risk Variable	Distribution	Param 1 (Mean/Min)	Param 2 (StdDev/Mode)	Param 3 (Max)	Lower Bound	Upper Bound	Source Sheet	Status
	Revenue Growth Rate	Normal	8.0%	5.0%		-10.0%	30.0%	Assumptions	Active
	COGS % of Revenue	Normal	55.0%	3.0%		30.0%	80.0%	Assumptions	Active
	OpEx Growth Rate	Normal	4.0%	2.0%		0.0%	15.0%	Assumptions	Active
	Price Change	Normal	0.0%	3.0%		-15.0%	15.0%	Assumptions	Active
	Interest Rate	Lognormal	5.0%	1.0%		1.0%	15.0%	Assumptions	Active
	Demand Volume	Triangular	350,000	500,000	700,000	350,000	700,000	Assumptions	Active
	Portfolio Return	Normal	10.0%	15.0%		-40.0%	50.0%	Assumptions	Active
	Tax Rate Variation	Uniform	20.0%		30.0%	20.0%	30.0%	Assumptions	Active
	DISTRIBUTION SELECTION GUIDE
	Criterion	Normal	Lognormal	Triangular	Uniform
	Symmetric data	✓ Best	✗	Possible	✓ Best
	Right-skewed data	✗	✓ Best	Possible	Possible
	Bounded [0,1]	✗	✗	✓	✓ Best
	Expert estimates only	Possible	✗	✓ Best	✗
	No info on shape	✗	✗	✗	✗
	Can be negative	✓ Best	✗	Possible	✗
	STANDARD NORMAL QUANTILE REFERENCE
	Confidence Level	Z-Score (1-tail)	Z-Score (2-tail)	Interpretation	Common Use
	90.0%	1.2816	1.6449	10% of outcomes worse	Moderate confidence
	95.0%	1.6449	1.9600	5% of outcomes worse	Industry standard VaR
	97.5%	1.9600	2.2414	2.5% of outcomes worse	Stress testing
	99.0%	2.3263	2.5758	1% of outcomes worse	Basel III / regulatory
	99.9%	3.0902	3.2905	0.1% of outcomes worse	Extreme tail risk
	NOTES
	• Green values reference the Assumptions sheet — changes propagate automatically
	• Distribution assignments drive the Simulation Engine random number generation
	• Z-scores are used for VaR and confidence interval calculations in Portfolio VaR sheet