distInfo=list(
Uniform=list(parName=c('lowBound','highBound'),
parLongName=c('lower bound','upper bound'),
parSymbol=c('a','b'),
constraints=c('a<b'),
url='https://en.wikipedia.org/wiki/Continuous_uniform_distribution',
note=NULL,
warning=NULL),
Normal=list(parName=c('mean','sd'),
parLongName=c('mean','standard deviation'),
parSymbol=c('mu','sigma'),
constraints=c('sigma>0'),
url='https://en.wikipedia.org/wiki/Normal_distribution',
note=NULL,
warning=NULL),
LogNormal=list(parName=c('meanlog','sdlog'),
parLongName=c('mean of log-variable','standard deviation of log-variable'),
parSymbol=c('mu','sigma'),
constraints=c('sigma>0'),
url='https://en.wikipedia.org/wiki/Log-normal_distribution',
note=NULL,
warning=NULL),
Gumbel=list(parName=c('location','scale'),
parLongName=c('location','scale'),
parSymbol=c('mu','sigma'),
constraints=c('sigma>0'),
url='https://en.wikipedia.org/wiki/Gumbel_distribution',
note=NULL,
warning=NULL),
Exponential1=list(parName=c('scale'),
parLongName=c('scale'),
parSymbol=c('sigma'),
constraints=c('sigma>0'),
url='https://en.wikipedia.org/wiki/Exponential_distribution',
note='Assumes a lower threshold equal to zero',
warning='The second parameter is the scale and NOT the rate (scale = 1/rate)'),
Exponential2=list(parName=c('threshold','scale'),
parLongName=c('threshold','scale'),
parSymbol=c('mu','sigma'),
constraints=c('sigma>0'),
url='https://en.wikipedia.org/wiki/Exponential_distribution',
note='This is just a shift of the standard exponential distribution (the latter corresponding to mu=0)',
warning='The second parameter is the scale and NOT the rate (scale = 1/rate)'),
GEV=list(parName=c('location','scale','shape'),
parLongName=c('location','scale','shape'),
parSymbol=c('mu','sigma','xi'),
constraints=c('sigma>0'),
url='https://en.wikipedia.org/wiki/Generalized_extreme_value_distribution',
note='xi=0 leads to the Gumbel distribution',
warning='xi < 0 corresponds to a heavy right tail, xi > 0 to a right-bounded distribution. This is THE OPPOSITE of the parameterization used in e.g. wikipedia or R package evd'),
GPD2=list(parName=c('scale','shape'),
parLongName=c('scale','shape'),
parSymbol=c('sigma','xi'),
constraints=c('sigma>0'),
url='https://en.wikipedia.org/wiki/Generalized_Pareto_distribution',
note='xi=0 leads to the exponential distribution; assumes a lower threshold equal to zero',
warning='xi < 0 corresponds to a heavy right tail, xi > 0 to a right-bounded distribution. This is THE OPPOSITE of the parameterization used in e.g. wikipedia or R package evd'),
GPD3=list(parName=c('threshold','scale','shape'),
parLongName=c('threshold','scale','shape'),
parSymbol=c('mu','sigma','xi'),
constraints=c('sigma>0'),
url='https://en.wikipedia.org/wiki/Generalized_Pareto_distribution',
note='xi=0 leads to the exponential distribution; GPD2 is a special case of GPD3 with mu=0',
warning='xi < 0 corresponds to a heavy right tail, xi > 0 to a right-bounded distribution. This is THE OPPOSITE of the parameterization used in e.g. wikipedia or R package evd'),
Poisson=list(parName=c('rate'),
parLongName=c('rate'),
parSymbol=c('lambda'),
constraints=c('lambda>0'),
url='https://en.wikipedia.org/wiki/Poisson_distribution',
note=NULL,
warning=NULL),
PearsonIII=list(parName=c('location','scale','shape'),
parLongName=c('location','scale','shape'),
parSymbol=c('mu','sigma','xi'),
constraints=c('sigma!=0','xi>0'),
url='https://www.rdocumentation.org/packages/PearsonDS/versions/1.2/topics/PearsonIII',
note=NULL,
warning=NULL),
LogPearsonIII=list(parName=c('locationlog','scalelog','shapelog'),
parLongName=c('location of log-variable','scale of log-variable','shape of log-variable'),
parSymbol=c('mu','sigma','xi'),
constraints=c('sigma!=0','xi>0'),
url='https://www.rdocumentation.org/packages/PearsonDS/versions/1.2/topics/PearsonIII',
note=NULL,
warning=NULL),
Gumbel_min=list(parName=c('location','scale'),
parLongName=c('location','scale'),
parSymbol=c('mu','sigma'),
constraints=c('sigma>0'),
url='https://en.wikipedia.org/wiki/Generalized_extreme_value_distribution#Modification_for_minima_rather_than_maxima',
note=c('Gumbel for minima is a distribution family distinct from the standard Gumbel.',
'It is derived from the equality: min(x)=-1*max(-x). Consequently:',
'f_{Gumbel_min}(x;mu,sigma) = f_{Gumbel}(-x;-mu,sigma)',
'F_{Gumbel_min}(x;mu,sigma) = 1 - F_{Gumbel}(-x;-mu,sigma)',
'Q_{Gumbel_min}(p;mu,sigma) = -1*Q_{Gumbel}(1-p;-mu,sigma)',
'RANDOM_{Gumbel_min}(mu,sigma) = -1*RANDOM_{Gumbel}(-mu,sigma)'),
warning=NULL),
GEV_min=list(parName=c('location','scale','shape'),
parLongName=c('location','scale','shape'),
parSymbol=c('mu','sigma','xi'),
constraints=c('sigma>0'),
url='https://en.wikipedia.org/wiki/Generalized_extreme_value_distribution#Modification_for_minima_rather_than_maxima',
note=c('GEV for minima is a distribution family distinct from the standard GEV.',
'It is derived from the equality: min(x)=-1*max(-x). Consequently:',
'f_{GEV_min}(x;mu,sigma,xi) = f_{GEV}(-x;-mu,sigma,xi)',
'F_{GEV_min}(x;mu,sigma,xi) = 1 - F_{GEV}(-x;-mu,sigma,xi)',
'Q_{GEV_min}(p;mu,sigma,xi) = -1*Q_{GEV}(1-p;-mu,sigma,xi)',
'RANDOM_{GEV_min}(mu,sigma,xi) = -1*RANDOM_{GEV}(-mu,sigma,xi)'),
warning='see GEV warning for parameterization of the shape parameter xi'),
GEV_min_pos=list(parName=c('location','scale'),
parLongName=c('location','scale'),
parSymbol=c('mu','sigma'),
constraints=c('sigma>0'),
url='https://en.wikipedia.org/wiki/Generalized_extreme_value_distribution#Modification_for_minima_rather_than_maxima',
note=c('This is a GEV_min with shape parameter fixed to xi=sigma/mu.',
'The resulting distribution has a lower bound equal to zero, which may be realistic for e.g. low flows.'),
warning='see GEV warning for parameterization of the shape parameter xi'),
FlatPrior=list(parName=c(),
parLongName=c(),
parSymbol=c(),
constraints=c(),
url='https://en.wikipedia.org/wiki/Prior_probability#Examples',
note='improper distribution corresponding to a uniform distribution on (-infinity;+infinity)',
warning='should only be used as a prior distribution'),
Triangle=list(parName=c('Peak','lowBound','highBound'),
parLongName=c('Peak','lower bound','upper bound'),
parSymbol=c('c','a','b'),
constraints=c('a<c<b'),
url='https://en.wikipedia.org/wiki/Triangular_distribution',
note=NULL,
warning=NULL)
)
save(distInfo,file='../data/distInfo.RData')
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