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Per.Andreas.Brodtkorb 11 years ago
parent 82008a52fb
commit b086a862db
1 changed files with 43 additions and 106 deletions
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pywafo/src/wafo/stats/distributions.py
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@ -772,65 +772,6 @@ def bd0(x, npr):
## Volumes I and II, Wiley & Sons, 1994. ## Volumes I and II, Wiley & Sons, 1994.
## Each continuous random variable as the following methods
##
## rvs -- Random Variates (alternatively calling the class could produce these)
## pdf -- PDF
## logpdf -- log PDF (more numerically accurate if possible)
## cdf -- CDF
## logcdf -- log of CDF
## sf -- Survival Function (1-CDF)
## logsf --- log of SF
## ppf -- Percent Point Function (Inverse of CDF)
## isf -- Inverse Survival Function (Inverse of SF)
## stats -- Return mean, variance, (Fisher's) skew, or (Fisher's) kurtosis
## nnlf -- negative log likelihood function (to minimize)
## fit -- Model-fitting
##
## Maybe Later
##
## hf --- Hazard Function (PDF / SF)
## chf --- Cumulative hazard function (-log(SF))
## psf --- Probability sparsity function (reciprocal of the pdf) in
## units of percent-point-function (as a function of q).
## Also, the derivative of the percent-point function.
## To define a new random variable you subclass the rv_continuous class
## and re-define the
##
## _pdf method which will be given clean arguments (in between a and b)
## and passing the argument check method
##
## If postive argument checking is not correct for your RV
## then you will also need to re-define
## _argcheck
## Correct, but potentially slow defaults exist for the remaining
## methods but for speed and/or accuracy you can over-ride
##
## _cdf, _ppf, _rvs, _isf, _sf
##
## Rarely would you override _isf and _sf but you could for numerical precision.
##
## Statistics are computed using numerical integration by default.
## For speed you can redefine this using
##
## _stats --- take shape parameters and return mu, mu2, g1, g2
## --- If you can't compute one of these return it as None
##
## --- Can also be defined with a keyword argument moments=<str>
## where <str> is a string composed of 'm', 'v', 's',
## and/or 'k'. Only the components appearing in string
## should be computed and returned in the order 'm', 'v',
## 's', or 'k' with missing values returned as None
##
## OR
##
## You can override
##
## _munp -- takes n and shape parameters and returns
## -- then nth non-central moment of the distribution.
##
def valarray(shape,value=nan,typecode=None): def valarray(shape,value=nan,typecode=None):
"""Return an array of all value. """Return an array of all value.
@ -996,6 +937,7 @@ class rv_generic(object):
raise TypeError("Too many input arguments.") raise TypeError("Too many input arguments.")
args = args[:self.numargs] args = args[:self.numargs]
if scale is None: if scale is None:
scale = 1.0 scale = 1.0
if loc is None: if loc is None:
@ -2502,7 +2444,6 @@ class rv_continuous(rv_generic):
except AttributeError: except AttributeError:
raise ValueError("%s is not a valid optimizer" % optimizer) raise ValueError("%s is not a valid optimizer" % optimizer)
vals = optimizer(func,x0,args=(ravel(data),),disp=0) vals = optimizer(func,x0,args=(ravel(data),),disp=0)
if restore is not None: if restore is not None:
vals = restore(args, vals) vals = restore(args, vals)
vals = tuple(vals) vals = tuple(vals)
@ -2932,9 +2873,7 @@ class beta_gen(rv_continuous):
def _rvs(self, a, b): def _rvs(self, a, b):
return mtrand.beta(a,b,self._size) return mtrand.beta(a,b,self._size)
def _pdf(self, x, a, b): def _pdf(self, x, a, b):
Px = (1.0-x)**(b-1.0) * x**(a-1.0) return np.exp(self._logpdf(x, a, b))
Px /= special.beta(a,b)
return Px
def _logpdf(self, x, a, b): def _logpdf(self, x, a, b):
logx = where((a==1) & (x==0), 0 , log(x)) logx = where((a==1) & (x==0), 0 , log(x))
log1mx = where((b==1) & (x==1), 0, log1p(-x)) log1mx = where((b==1) & (x==1), 0, log1p(-x))
@ -3005,13 +2944,13 @@ class betaprime_gen(rv_continuous):
u2 = gamma.rvs(b,size=self._size) u2 = gamma.rvs(b,size=self._size)
return (u1 / u2) return (u1 / u2)
def _pdf(self, x, a, b): def _pdf(self, x, a, b):
return 1.0/special.beta(a,b)*x**(a-1.0)/(1+x)**(a+b) return np.exp(self._logpdf(x, a, b))
def _logpdf(self, x, a, b): def _logpdf(self, x, a, b):
return (a-1.0)*log(x) - (a+b)*log1p(x) - log(special.beta(a,b)) return (a-1.0)*log(x) - (a+b)*log1p(x) - log(special.beta(a,b))
def _cdf_skip(self, x, a, b): def _cdf_skip(self, x, a, b):
# remove for now: special.hyp2f1 is incorrect for large a # remove for now: special.hyp2f1 is incorrect for large a
x = where(x==1.0, 1.0-1e-6,x) x = where(x==1.0, 1.0-1e-6,x)
return power(x,a)*special.hyp2f1(a+b,a,1+a,-x)/a/special.beta(a,b) return pow(x,a)*special.hyp2f1(a+b,a,1+a,-x)/a/special.beta(a,b)
def _munp(self, n, a, b): def _munp(self, n, a, b):
if (n == 1.0): if (n == 1.0):
return where(b > 1, a/(b-1.0), inf) return where(b > 1, a/(b-1.0), inf)
@ -3397,7 +3336,7 @@ class dweibull_gen(rv_continuous):
return where(x > 0, 1-Cx1, Cx1) return where(x > 0, 1-Cx1, Cx1)
def _ppf_skip(self, q, c): def _ppf_skip(self, q, c):
fac = where(q<=0.5,2*q,2*q-1) fac = where(q<=0.5,2*q,2*q-1)
fac = power(asarray(log(1.0/fac)),1.0/c) fac = pow(asarray(log(1.0/fac)),1.0/c)
return where(q>0.5,fac,-fac) return where(q>0.5,fac,-fac)
def _stats(self, c): def _stats(self, c):
var = gam(1+2.0/c) var = gam(1+2.0/c)
@ -3582,7 +3521,7 @@ class exponpow_gen(rv_continuous):
def _isf(self, x, b): def _isf(self, x, b):
return (log1p(-log(x)))**(1./b) return (log1p(-log(x)))**(1./b)
def _ppf(self, q, b): def _ppf(self, q, b):
return power(log1p(-log1p(-q)), 1.0/b) return pow(log1p(-log1p(-q)), 1.0/b)
exponpow = exponpow_gen(a=0.0, name='exponpow', shapes='b') exponpow = exponpow_gen(a=0.0, name='exponpow', shapes='b')
@ -3806,13 +3745,13 @@ class frechet_r_gen(rv_continuous):
return phati return phati
def _pdf(self, x, c): def _pdf(self, x, c):
return c*power(x,c-1)*exp(-power(x,c)) return c*pow(x,c-1)*exp(-pow(x,c))
def _logpdf(self, x, c): def _logpdf(self, x, c):
return log(c) + (c-1)*log(x) - power(x,c) return log(c) + (c-1)*log(x) - pow(x,c)
def _cdf(self, x, c): def _cdf(self, x, c):
return -expm1(-power(x,c)) return -expm1(-pow(x,c))
def _ppf(self, q, c): def _ppf(self, q, c):
return power(-log1p(-q),1.0/c) return pow(-log1p(-q),1.0/c)
def _munp(self, n, c): def _munp(self, n, c):
return special.gamma(1.0+n*1.0/c) return special.gamma(1.0+n*1.0/c)
def _entropy(self, c): def _entropy(self, c):
@ -3827,6 +3766,7 @@ frechet_r = frechet_r_gen(a=0.0, name='frechet_r', shapes='c')
weibull_min = frechet_r_gen(a=0.0, name='weibull_min', shapes='c') weibull_min = frechet_r_gen(a=0.0, name='weibull_min', shapes='c')
class frechet_l_gen(rv_continuous): class frechet_l_gen(rv_continuous):
"""A Frechet left (or Weibull maximum) continuous random variable. """A Frechet left (or Weibull maximum) continuous random variable.
@ -3849,11 +3789,11 @@ class frechet_l_gen(rv_continuous):
""" """
def _pdf(self, x, c): def _pdf(self, x, c):
return c*power(-x,c-1)*exp(-power(-x,c)) return c*pow(-x,c-1)*exp(-pow(-x,c))
def _cdf(self, x, c): def _cdf(self, x, c):
return exp(-power(-x,c)) return exp(-pow(-x,c))
def _ppf(self, q, c): def _ppf(self, q, c):
return -power(-log(q),1.0/c) return -pow(-log(q),1.0/c)
def _munp(self, n, c): def _munp(self, n, c):
val = special.gamma(1.0+n*1.0/c) val = special.gamma(1.0+n*1.0/c)
if (int(n) % 2): if (int(n) % 2):
@ -3899,7 +3839,7 @@ class genlogistic_gen(rv_continuous):
Cx = (1+exp(-x))**(-c) Cx = (1+exp(-x))**(-c)
return Cx return Cx
def _ppf(self, q, c): def _ppf(self, q, c):
vals = -log(power(q,-1.0/c)-1) vals = -log(pow(q,-1.0/c)-1)
return vals return vals
def _stats(self, c): def _stats(self, c):
zeta = special.zeta zeta = special.zeta
@ -4194,7 +4134,7 @@ class genextreme_gen(rv_continuous):
return where(abs(c)==inf, 0, 1) #True #(c!=0) return where(abs(c)==inf, 0, 1) #True #(c!=0)
def _pdf(self, x, c): def _pdf(self, x, c):
## ex2 = 1-c*x ## ex2 = 1-c*x
## pex2 = power(ex2,1.0/c) ## pex2 = pow(ex2,1.0/c)
## p2 = exp(-pex2)*pex2/ex2 ## p2 = exp(-pex2)*pex2/ex2
## return p2 ## return p2
return exp(self._logpdf(x, c)) return exp(self._logpdf(x, c))
@ -4610,7 +4550,7 @@ class halflogistic_gen(rv_continuous):
if n==2: return pi*pi/3.0 if n==2: return pi*pi/3.0
if n==3: return 9*_ZETA3 if n==3: return 9*_ZETA3
if n==4: return 7*pi**4 / 15.0 if n==4: return 7*pi**4 / 15.0
return 2*(1-power(2.0,1-n))*special.gamma(n+1)*special.zeta(n,1) return 2*(1-pow(2.0,1-n))*special.gamma(n+1)*special.zeta(n,1)
def _entropy(self): def _entropy(self):
return 2-log(2) return 2-log(2)
halflogistic = halflogistic_gen(a=0.0, name='halflogistic') halflogistic = halflogistic_gen(a=0.0, name='halflogistic')
@ -4818,7 +4758,7 @@ class invweibull_gen(rv_continuous):
xc1 = x**(-c) xc1 = x**(-c)
return exp(-xc1) return exp(-xc1)
def _ppf(self, q, c): def _ppf(self, q, c):
return power(-log(q),asarray(-1.0/c)) return pow(-log(q),asarray(-1.0/c))
def _entropy(self, c): def _entropy(self, c):
return 1+_EULER + _EULER / c - log(c) return 1+_EULER + _EULER / c - log(c)
invweibull = invweibull_gen(a=0, name='invweibull', shapes='c') invweibull = invweibull_gen(a=0, name='invweibull', shapes='c')
@ -5164,7 +5104,7 @@ class lognorm_gen(rv_continuous):
for ``x > 0``, ``s > 0``. for ``x > 0``, ``s > 0``.
If log x is normally distributed with mean mu and variance sigma**2, If log x is normally distributed with mean mu and variance sigma**2,
then x is log-normally distributed with shape paramter sigma and scale then x is log-normally distributed with shape parameter sigma and scale
parameter exp(mu). parameter exp(mu).
%(example)s %(example)s
@ -5174,8 +5114,6 @@ class lognorm_gen(rv_continuous):
return exp(s * norm.rvs(size=self._size)) return exp(s * norm.rvs(size=self._size))
def _pdf(self, x, s): def _pdf(self, x, s):
return exp(self._logpdf(x, s)) return exp(self._logpdf(x, s))
#Px = exp(-log(x)**2 / (2*s**2))
#return Px / (s*x*sqrt(2*pi))
def _logpdf(self, x, s): def _logpdf(self, x, s):
return -log(x)**2 / (2*s**2) + np.where(x==0 , 0, - log(s*x*sqrt(2*pi))) return -log(x)**2 / (2*s**2) + np.where(x==0 , 0, - log(s*x*sqrt(2*pi)))
def _cdf(self, x, s): def _cdf(self, x, s):
@ -5303,8 +5241,8 @@ class mielke_gen(rv_continuous):
def _cdf(self, x, k, s): def _cdf(self, x, k, s):
return x**k / (1.0+x**s)**(k*1.0/s) return x**k / (1.0+x**s)**(k*1.0/s)
def _ppf(self, q, k, s): def _ppf(self, q, k, s):
qsk = power(q,s*1.0/k) qsk = pow(q,s*1.0/k)
return power(qsk/(1.0-qsk),1.0/s) return pow(qsk/(1.0-qsk),1.0/s)
mielke = mielke_gen(a=0.0, name='mielke', shapes="k, s") mielke = mielke_gen(a=0.0, name='mielke', shapes="k, s")
@ -5340,7 +5278,6 @@ class nakagami_gen(rv_continuous):
g2 = -6*mu**4*nu + (8*nu-2)*mu**2-2*nu + 1 g2 = -6*mu**4*nu + (8*nu-2)*mu**2-2*nu + 1
g2 /= nu*mu2**2.0 g2 /= nu*mu2**2.0
return mu, mu2, g1, g2 return mu, mu2, g1, g2
nakagami = nakagami_gen(a=0.0, name="nakagami", shapes='nu') nakagami = nakagami_gen(a=0.0, name="nakagami", shapes='nu')
@ -5598,7 +5535,7 @@ class pareto_gen(rv_continuous):
def _cdf(self, x, b): def _cdf(self, x, b):
return 1 - x**(-b) return 1 - x**(-b)
def _ppf(self, q, b): def _ppf(self, q, b):
return power(1-q, -1.0/b) return pow(1-q, -1.0/b)
def _stats(self, b, moments='mv'): def _stats(self, b, moments='mv'):
mu, mu2, g1, g2 = None, None, None, None mu, mu2, g1, g2 = None, None, None, None
if 'm' in moments: if 'm' in moments:
@ -5858,12 +5795,12 @@ class powerlognorm_gen(rv_continuous):
""" """
def _pdf(self, x, c, s): def _pdf(self, x, c, s):
return c/(x*s)*norm.pdf(log(x)/s)*power(norm.cdf(-log(x)/s),c*1.0-1.0) return c/(x*s)*norm.pdf(log(x)/s)*pow(norm.cdf(-log(x)/s),c*1.0-1.0)
def _cdf(self, x, c, s): def _cdf(self, x, c, s):
return 1.0 - power(norm.cdf(-log(x)/s),c*1.0) return 1.0 - pow(norm.cdf(-log(x)/s),c*1.0)
def _ppf(self, q, c, s): def _ppf(self, q, c, s):
return exp(-s*norm.ppf(power(1.0-q,1.0/c))) return exp(-s*norm.ppf(pow(1.0-q,1.0/c)))
powerlognorm = powerlognorm_gen(a=0.0, name="powerlognorm", shapes="c, s") powerlognorm = powerlognorm_gen(a=0.0, name="powerlognorm", shapes="c, s")
@ -5894,7 +5831,7 @@ class powernorm_gen(rv_continuous):
def _cdf(self, x, c): def _cdf(self, x, c):
return 1.0-_norm_cdf(-x)**(c*1.0) return 1.0-_norm_cdf(-x)**(c*1.0)
def _ppf(self, q, c): def _ppf(self, q, c):
return -norm.ppf(power(1.0-q,1.0/c)) return -norm.ppf(pow(1.0-q,1.0/c))
powernorm = powernorm_gen(name='powernorm', shapes="c") powernorm = powernorm_gen(name='powernorm', shapes="c")
@ -6064,9 +6001,9 @@ class reciprocal_gen(rv_continuous):
def _cdf(self, x, a, b): def _cdf(self, x, a, b):
return (log(x)-log(a)) / self.d return (log(x)-log(a)) / self.d
def _ppf(self, q, a, b): def _ppf(self, q, a, b):
return a*power(b*1.0/a,q) return a*pow(b*1.0/a,q)
def _munp(self, n, a, b): def _munp(self, n, a, b):
return 1.0/self.d / n * (power(b*1.0,n) - power(a*1.0,n)) return 1.0/self.d / n * (pow(b*1.0,n) - pow(a*1.0,n))
def _entropy(self,a,b): def _entropy(self,a,b):
return 0.5*log(a*b)+log(log(b/a)) return 0.5*log(a*b)+log(log(b/a))
reciprocal = reciprocal_gen(name="reciprocal", shapes="a, b") reciprocal = reciprocal_gen(name="reciprocal", shapes="a, b")
@ -6343,7 +6280,7 @@ class tukeylambda_gen(rv_continuous):
def _entropy(self, lam): def _entropy(self, lam):
def integ(p): def integ(p):
return log(power(p,lam-1)+power(1-p,lam-1)) return log(pow(p,lam-1)+pow(1-p,lam-1))
return integrate.quad(integ,0,1)[0] return integrate.quad(integ,0,1)[0]
tukeylambda = tukeylambda_gen(name='tukeylambda', shapes="lam") tukeylambda = tukeylambda_gen(name='tukeylambda', shapes="lam")

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