def _get_norms(self, a, b):
_nb = _norm_cdf(b)
_na = _norm_cdf(a)
_sb = _norm_sf(b)
_sa = _norm_sf(a)
_delta = np.where(a > 0, _sa - _sb, _nb - _na)
return _na, _nb, _sa, _sb, _delta, np.log(_delta)
def _logpdf(self, x, betaL, betaH, mL, mH):
"""
Return the log of the PDF of the double-sided crystalball function.
"""
N = 1.0 / (
mL / betaL / (mL - 1) * np.exp(-0.5 * betaL * betaL)
+ mH / betaH / (mH - 1) * np.exp(-0.5 * betaH * betaH)
+ _norm_pdf_C * (_norm_cdf(betaH) - _norm_cdf(-betaL))
)
def core(x, beta, m):
return -0.5 * x * x
def tail(x, beta, m):
return (
m * np.log(m / beta)
- 0.5 * beta * beta
- m * np.log(m / beta - beta - x)
)
def lhs(x, betaL, betaH, mL, mH):
return tail(x, betaL, mL)
def rhs(x, betaL, betaH, mL, mH):
return _lazywhere(x < betaH, (-x, betaH, mH), f=core, f2=tail)
return np.log(N) + _lazywhere(
x > -betaL, (x, betaL, betaH, mL, mH), f=rhs, f2=lhs
)
def _argcheck(self, a, b):
self.a = a
self.b = b
self._nb = _norm_cdf(b)
self._na = _norm_cdf(a)
self._sb = _norm_sf(b)
self._sa = _norm_sf(a)
self._delta = self._nb - self._na
idx = self.a > 0
self._delta[idx] = -(self._sb[idx] - self._sa[idx])
self._logdelta = np.log(self._delta)
return (a != b)
def _argcheck(self, a, b):
self.a = a
self.b = b
self._cdfb = crv_helper._norm_cdf(b)
self._cdfa = crv_helper._norm_cdf(a)
self._cdfminb = crv_helper._norm_cdf(-b)
self._cdfmina = crv_helper._norm_cdf(-a)
self._delta = np.where(
self.a > 0, -(self._cdfminb - self._cdfmina), self._cdfb - self._cdfa
)
self._logdelta = np.log(self._delta)
return a != b
def _argcheck(self, a, b):
self.a = a
self.b = b
self._nb = _norm_cdf(b)
self._na = _norm_cdf(a)
self._sb = _norm_sf(b)
self._sa = _norm_sf(a)
self._delta = self._nb - self._na
idx = self.a > 0
self._delta[idx] = -(self._sb[idx] - self._sa[idx])
self._logdelta = np.log(self._delta)
return (a != b)
def __init__(self, mean, sigma, bounds=None):
self.mean = mean
self.sigma = sigma
self._bounds = bounds
self._norm = 1.
if bounds:
lo, hi = bounds
a, b = (lo - mean) / sigma, (hi - mean) / sigma
self.distribution = scipy.stats.truncnorm(a, b, loc=mean, scale=sigma)
self.norm = _norm_cdf(b) - _norm_cdf(a)
self.lognorm = np.log(self.norm)
else:
self.distribution = scipy.stats.norm(mean, sigma)
self.norm = 1.
self.lognorm = 0.
def core(p, betaL, betaH, mL, mH):
CL = inttail(betaL, mL)
CH = inttail(betaH, mH)
C = CL + CH
N = 1 / (C + intcore(betaL, betaH))
return _norm_ppf(
_norm_cdf(-betaL) + (1 / _norm_pdf_C) * (p / N - CL))
def __init__(self, mean, sigma, bounds=None):
self.mean = mean
self.sigma = sigma
self._bounds = bounds
self._norm = 1.0
if bounds:
lo, hi = bounds
a, b = (lo - mean) / sigma, (hi - mean) / sigma
self.distribution = scipy.stats.truncnorm(a, b, loc=mean, scale=sigma)
self.norm = _norm_cdf(b) - _norm_cdf(a)
self.lognorm = np.log(self.norm)
else:
self.distribution = scipy.stats.norm(mean, sigma)
self.norm = 1.0
self.lognorm = 0.0
def _cdf(self, x, betaL, betaH, mL, mH):
"""
Return CDF of the double-sided crystalball function
"""
N = 1.0 / (
mL / betaL / (mL - 1) * np.exp(-0.5 * betaL * betaL)
+ mH / betaH / (mH - 1) * np.exp(-0.5 * betaH * betaH)
+ _norm_pdf_C * (_norm_cdf(betaH) - _norm_cdf(-betaL))
)
def inttail(beta, m):
return m / beta / (m - 1) * np.exp(-0.5 * beta * beta)
def intcore(betaL, betaH):
return _norm_pdf_C * (_norm_cdf(betaH) - _norm_cdf(-betaL))
def tail(x, beta, m):
return (
(m / beta) ** m
* np.exp(-0.5 * beta * beta)
* (m / beta - beta - x) ** (1 - m)
/ (m - 1)
)
def hightail(x, betaL, betaH, mL, mH):
return (
inttail(betaL, mL)
+ intcore(betaL, betaH)
+ inttail(betaH, mH)
- tail(-x, betaH, mH)
)
def core(x, betaL, betaH, mL, mH):
return inttail(betaL, mL) + _norm_pdf_C * (_norm_cdf(x) - _norm_cdf(-betaL))
def lhs(x, betaL, betaH, mL, mH):
return tail(x, betaL, mL)
def rhs(x, betaL, betaH, mL, mH):
return _lazywhere(x < betaH, (x, betaL, betaH, mL, mH), f=core, f2=hightail)
return N * _lazywhere(x > -betaL, (x, betaL, betaH, mL, mH), f=rhs, f2=lhs)
def test_johnson_quantile_fit():
quantile_pts = np.array(_norm_cdf([-1.5, -0.5, 0.5, 1.5]))
test_quantiles = [[1, 1.2, 1.4, 10], [1, 1.2, 1.4, 3], [-2, -1, 1, 2]]
for quantiles_in in test_quantiles:
dist = j_util._fit_johnson_by_quantiles(quantiles_in)
quantiles_out = dist.ppf(quantile_pts)
npt.assert_allclose(
quantiles_in,
quantiles_out,
decimal,
err_msg=f'Fitting johnson distribution by quartiles failed for test '
f'quartiles {quantiles_in}')
def _cdf(self, x, a, b):
return (crv_helper._norm_cdf(x) - self._cdfa) / self._delta
def intcore(betaL, betaH):
return _norm_pdf_C * (_norm_cdf(betaH) - _norm_cdf(-betaL))
def core(x, betaL, betaH, mL, mH):
return inttail(
betaL, mL) + _norm_pdf_C * (_norm_cdf(x) - _norm_cdf(-betaL))
