def ipareto(prob, lam, xm=1.0):
"""
The inverse of the Pareto distribution:
f = lam * xm**lam / x**(lam+1)
F = 1 - (xm/x)**lam
x in [xm, inf)
lam > 0
For lam < 1 all moments are infinite
For lam < 2 all moments are infinite except for the mean
"""
_assertprob(prob, 'ipareto')
assert lam > 0.0, "shape parameter lambda in ipareto must be positive!"
assert xm >= 0.0, \
"left support limit parameter xm must not be negative in ipareto!"
q = 1.0 - prob
if q == 0.0: return float('inf')
x = xm * safepow(q, -1.0/lam)
x = kept_within(xm, x)
return x
def ipareto_zero(prob, lam, xm=1.0):
"""
The inverse of the Pareto distribution with the support shifted to [0, inf):
f = lam * xm**lam / (x+xm)**(lam+1)
F = 1 - [xm/(x+xm)]**lam
x in [0, inf)
lam > 0
For lam < 1 all moments are infinite
For lam < 2 all moments are infinite except for the mean
"""
_assertprob(prob, 'ipareto_zero')
assert lam > 0.0, "shape parameter lambda in ipareto_zero must be positive!"
textxm1 = "left support limit parameter xm of unshifted in ipareto_zero"
textxm2 = "distribution must not be negative in ipareto_zero!"
assert xm >= 0.0, textxm1 + textxm2
q = 1.0 - prob
if q == 0.0: return float('inf')
x = xm * (safepow(q, -1.0/lam) - 1.0)
x = kept_within(0.0, x)
return x
def iweibull(prob, c, scale=1.0):
"""
The inverse of the Weibull distribution:
F = 1 - exp[-(x/s)**c]
x >= 0, s >= 0, c >= 1
"""
if c == 1.0:
x = iexpo(prob, scale)
else:
_assertprob(prob, 'iweibull')
# ---
assert c >= 1.0, \
"shape parameter in iweibull must not be smaller than 1.0!"
assert scale >= 0.0, "scale parameter in iweibull must not be negative!"
x = scale * safepow(-safelog(1.0-prob), 1.0/c)
#x = kept_within(0.0, x) # Not really needed
return x
