The ADSM team has prepared a detailed explanation of all the types of Probability Density Functions (PDFs) used in ADSM.

Download Probability Density Functions.docx

Naming of PDF parameters is inconsistent between reference guides.

• The XML parameter file format used by NAADSM adopted its naming from the GNU Scientific Library.
• The database fields in NAADSM/ADSM adopted their naming from Risk Analysis: A Quantitative Guide, 2nd edition, by Vose.
• The graphical displays in ADSM use the functions from SciPy.

The table below shows how the parameter names match up. In some cases, transformations are required.

• When there is an expression in the “ADSM Database” column, the expression assumes we are taking the parameters from NAADSM XML and placing them into the database when importing a NAADSM legacy scenario.
• When there is an expression in the “SciPy” column, the expression assumes we are taking the parameters from the ADSM database and creating a SciPy object. SciPy uses a mix of positional and named arguments.

PDF Type	NAADSM XML	ADSM Database	SciPy
Bernoulli	p	p	scipy.stats.bernoulli(  p )
Beta	alpha beta location scale	alpha alpha2 min max	scipy.stats.beta(  alpha,  alpha2,  loc=min,  scale=max-min )
Beta-pert	min mode max	min mode max	d = (min + 4*mode + max)/6 alpha = 6*((d - min)/(max - min)) beta = 6*((max - d)/(max - min)) scipy.stats.beta(  alpha,  beta,  loc=min,  scale=max-min )
Binomial	n p	s p	scipy.stats.binom(  s,  p )
Discrete Uniform	min max	min max	scipy.stats.randint(  min,  max )
Exponential	mean	mean	scipy.stats.expon(  scale=mean )
Fixed Value	no parameter name	mode	Not offered in SciPy? Use a narrow uniform instead
Gamma	alpha beta	alpha beta	scipy.stats.gamma(  alpha,  scale=beta,  loc=0 )
Gaussian	mean stddev	mean std_dev	scipy.stats.norm(  loc=mean,  scale=std_dev )
Histogram
Hypergeometric	d m n	d m n	scipy.stats.hypergeom(  m,  d,  n )
Inverse Gaussian	mu lambda	mean shape	Shape/lambda parameter not supported in SciPy?
Logistic	location scale	location scale	scipy.stats.logistic(  loc=location,  scale=scale )
Log-logistic	location scale shape	location scale shape	scipy.stats.fisk(  shape,  loc=location,  scale=scale )
Lognormal	zeta sigma	mean = exp( zeta + sigma2/2 ) std_dev = sqrt(exp( 2*zeta + sigma2 ) * (exp(sigma2) - 1))	zeta = ln(mean²/sqrt(std_dev²+mean²)) sigma = sqrt(ln((std_dev²+mean²)/mean²)) scipy.stats.lognorm(  sigma,  scale=exp(zeta) )
Negative Binomial	s p	s p	scipy.stats.nbinom(  s,  p )
Pareto	theta a	theta a	scipy.stats.pareto(  theta,  scale=a )
Pearson V	alpha beta	alpha beta	scipy.stats.invgamma(  alpha,  scale=beta )
Piecewise
Poisson	mean	mean	scipy.stats.poisson(  mean )
Triangular	a c b	min mode max	scipy.stats.triang(  (mode-min)/(max-min),  loc=min,  scale=max-min )
Uniform	a b	min max	scipy.stats.uniform(  loc=min,  scale=max-min )
Weibull	alpha beta	alpha beta	scipy.stats.weibull_min(  alpha,  scale=beta )