def get_stats(name, **kwargs):
'''
Takes a distribution name and paras,
and returns key statistics.
Note: for stat-getting the only choice
is to use *scipy*. We need to be careful
to ensure the parametrization matches
with that used in our get_generator fn,
which runs on numpy Generator methods.
Thus, kwargs here follow *numpy* namings.
'''
_sp = "mv" # moment specification for scipy.stats computations.
if name == "lognormal":
mean, var = lognorm.stats(s=kwargs["sigma"],
scale=np.exp(kwargs["mean"]),
moments=_sp)
elif name == "normal":
mean, var = norm.stats(loc=kwargs["loc"],
scale=kwargs["scale"],
moments=_sp)
elif name == "pareto":
mean, var = pareto.stats(b=kwargs["shape"],
scale=kwargs["scale"],
moments=_sp)
else:
raise ValueError("Please provide a proper distribution name.")
return {"mean": mean, "var": var}
def __init__(self, shape_parameter):
self.shape_parameter = shape_parameter
if self.shape_parameter is not None:
self.bounds = np.array([0.0, np.inf])
if self.shape_parameter > 0:
mean, var, skew, kurt = lognorm.stats(s=self.shape_parameter,
moments='mvsk')
self.parent = lognorm(s=self.shape_parameter)
self.mean = mean
self.variance = var
self.skewness = skew
self.kurtosis = kurt
self.x_range_for_pdf = np.linspace(0., 20.,
RECURRENCE_PDF_SAMPLES)
def main(sharp):
fig, ax = plt.subplots(1, 1)
mean, var, skew, kurt = lognorm.stats(s, moments='mvsk')
x = logNrm_dist(s)
ax.plot(x, lognorm.pdf(x, s), 'r-', lw=5, alpha=0.6, label='lognorm pdf')
# freeze the dist and display the frozen pdf
rv = lognorm(s)
ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
# gen radom numbers
r = lognorm.rvs(s, size=1000)
#ax.hist(r, histtype='stepfilled', alpha=0.2)
ax.legend(loc='best', frameon=False)
plt.show()
def get_population_average_estimate(param, shape):
size = 100000
if shape == 'normal' or shape == 'contaminated normal':
mu = 0
elif shape == 'lognormal':
mu = lognorm.stats(param, moments='m')
elif shape == 'contaminated chi-squared':
# mu = chi2.stats(4, 0, param, moments='m')
data = chi2.rvs(4, size=size)
contam_inds = np.random.randint(size, size=int(param * size))
data[contam_inds] *= 10
mu = np.mean(data)
elif shape == 'exponential':
mu = expon.stats(0, param, moments='m')
return mu
#Next, I am interested in understand how lognormal fits would approximate
#the data instead of skewed normal fits, so I repeat the analysis with lognormal fits
plt.figure(6)
plt.title('Lognormal distributions of distance bins')
plt.ylabel('Sizes (m)')
plt.xlabel('Distance (m)')
plt.ylim(0, 0.125)
n = 1
lognorm_mean_distance = []
lognorm_var_distance = []
lognorm_skew_distance = []
lognorm_kurt_distance = []
for bins in size_nest_distances:
if len(bins) > 10:
s, loc, scale = lognorm.fit(bins)
mean, var, skew, kurt = lognorm.stats(s, loc, scale, moments='mvsk')
lognorm_mean_distance.append(mean)
lognorm_var_distance.append(var)
lognorm_skew_distance.append(skew)
lognorm_kurt_distance.append(kurt)
pdf = lognorm.pdf(x, s, loc, scale)
plt.plot(x, pdf, label='{}'.format(
n)) #In this plot I am plotting all distributions together
n += 1
plt.legend()
plt.figure(7)
plt.title('Lognormal distributions of distance bins')
plt.ylabel('Sizes (m)')
plt.xlabel('Distance bin (m)')
n = 1
# @Time : 2020/5/14 22:07 # @Author : gzzang # @File : lognorm # @Project : notebook from scipy.stats import lognorm import matplotlib.pyplot as plt import numpy as np import pdb fig, ax = plt.subplots(1, 1) s = 0.954 s = 0.5 mean, var, skew, kurt = lognorm.stats(s, moments='mvsk') x = np.linspace(lognorm.ppf(0.01, s), lognorm.ppf(0.99, s), 100) ax.plot(x, lognorm.pdf(x, s), 'r-', lw=5, alpha=0.6, label='lognorm pdf') rv = lognorm(s) ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf') vals = lognorm.ppf([0.001, 0.5, 0.999], s) print(np.allclose([0.001, 0.5, 0.999], lognorm.cdf(vals, s))) print(np.allclose(a=[1.1000000000001, 1.2], b=[1.1, 1.2])) # pdb.set_trace() r = lognorm.rvs(s, size=1000) sigma = s mu = 0
def hesap(ax, bx):
z, k, m, n, p, t = 0, 0, 0, 0, 0, 0
studentGuvenAlt, aadmGuvenAlt, maadGuvenAlt, madmGuvenAlt, johnsonGuvenAlt, chenGuvenAlt = list(
), list(), list(), list(), list(), list()
studentGuvenUst, aadmGuvenUst, maadGuvenUst, madmGuvenUst, johnsonGuvenUst, chenGuvenUst = list(
), list(), list(), list(), list(), list()
workbook = xlwt.Workbook()
sayfa = workbook.add_sheet("Sayfa1")
sayfa.write(0, 1, "Student-t")
sayfa.write(0, 3, "AADM-t")
sayfa.write(0, 5, "MAAD-t")
sayfa.write(0, 7, "MADM-t")
sayfa.write(0, 9, "Johnson-t")
sayfa.write(0, 11, "Chen-t")
for item in range(0, 13):
if item == 0:
sayfa.write(1, 0, "n")
elif item % 2 == 0:
sayfa.write(1, item, "AW")
else:
sayfa.write(1, item, "CP")
for i in range(5, 10):
for j in range(1, 2501):
x = lognorm.rvs(bx, size=i)
mean, var, skew, kurt = lognorm.stats(bx, moments='mvsk')
meanx = round(statistics.mean(x), 4)
medianx = round(statistics.median(x), 4)
stdevx = round(statistics.stdev(x), 4)
aadmx = round((math.sqrt(math.pi / 2) / i) * sum(abs(x - medianx)),
4)
maadx = round(statistics.median(abs(x - meanx)), 4)
madmx = round(statistics.median(abs(x - medianx)), 4)
toplam = 0
for k in range(0, i):
toplam = toplam + ((x[k] - meanx)**3)
m3 = (i / ((i - 1) * (i - 2))) * toplam
studentalt = round(meanx - cell[i - 5] * stdevx / math.sqrt(i), 4)
studentust = round(meanx + cell[i - 5] * stdevx / math.sqrt(i), 4)
aadmalt = round(meanx - cell[i - 5] * aadmx / math.sqrt(i), 4)
aadmust = round(meanx + cell[i - 5] * aadmx / math.sqrt(i), 4)
maadalt = round(meanx - cell[i - 5] * maadx / math.sqrt(i), 4)
maadust = round(meanx + cell[i - 5] * maadx / math.sqrt(i), 4)
madmalt = round(meanx - cell[i - 5] * madmx / math.sqrt(i), 4)
madmust = round(meanx + cell[i - 5] * madmx / math.sqrt(i), 4)
johnsonalt = round((meanx + (m3 / (6 * i * (stdevx**2)))) -
cell[i - 5] * math.sqrt(i) * stdevx, 4)
johnsonust = round((meanx + (m3 / (6 * i * (stdevx**2)))) +
cell[i - 5] * math.sqrt(i) * stdevx, 4)
chenalt = round(meanx - (cell[i - 5] + (
((m3 / (stdevx**3)) *
(1 + 2 * (cell[i - 5]**2))) / (6 * math.sqrt(i))) + (
(((m3 / (stdevx**3))**2) *
(cell[i - 5] + 2 *
(cell[i - 5])**2) / 9 * i)) + math.sqrt(i) * stdevx))
chenust = round(meanx + (cell[i - 5] + (
((m3 / (stdevx**3)) *
(1 + 2 * (cell[i - 5]**2))) / (6 * math.sqrt(i))) + (
(((m3 / (stdevx**3))**2) *
(cell[i - 5] + 2 *
(cell[i - 5])**2) / 9 * i)) + math.sqrt(i) * stdevx))
studentGuvenAlt.append(studentalt)
studentGuvenUst.append(studentust)
aadmGuvenAlt.append(aadmalt)
aadmGuvenUst.append(aadmust)
maadGuvenAlt.append(maadalt)
maadGuvenUst.append(maadust)
madmGuvenAlt.append(madmalt)
madmGuvenUst.append(madmust)
johnsonGuvenAlt.append(johnsonalt)
johnsonGuvenUst.append(johnsonust)
chenGuvenAlt.append(chenalt)
chenGuvenUst.append(chenust)
if studentalt <= mean <= studentust:
z = z + 1
if aadmalt <= mean <= aadmust:
k = k + 1
if madmalt <= mean <= madmust:
m = m + 1
if maadalt <= mean <= maadust:
n = n + 1
if johnsonalt <= mean <= johnsonust:
p = p + 1
if chenalt <= mean <= chenust:
t = t + 1
sayfa.write(i - 3, 0, f"{i}")
sayfa.write(i - 3, 1, f"{round(z / 2500, 4)}")
sayfa.write(
i - 3, 2,
f"{round(statistics.mean(studentGuvenUst) - statistics.mean(studentGuvenAlt), 4)}"
)
sayfa.write(i - 3, 3, f"{round(k / 2500, 4)}")
sayfa.write(
i - 3, 4,
f"{round(statistics.mean(aadmGuvenUst) - statistics.mean(aadmGuvenAlt), 4)}"
)
sayfa.write(i - 3, 5, f"{round(n / 2500, 4)}")
sayfa.write(
i - 3, 6,
f"{round(statistics.mean(maadGuvenUst) - statistics.mean(maadGuvenAlt), 4)}"
)
sayfa.write(i - 3, 7, f"{round(m / 2500, 4)}")
sayfa.write(
i - 3, 8,
f"{round(statistics.mean(madmGuvenUst) - statistics.mean(madmGuvenAlt), 4)}"
)
sayfa.write(i - 3, 9, f"{round(p / 2500, 4)}")
sayfa.write(
i - 3, 10,
f"{round(statistics.mean(johnsonGuvenUst) - statistics.mean(johnsonGuvenAlt), 4)}"
)
sayfa.write(i - 3, 11, f"{round(t / 2500, 4)}")
sayfa.write(
i - 3, 12,
f"{round(statistics.mean(chenGuvenUst) - statistics.mean(chenGuvenAlt), 4)}"
)
workbook.save(f'L({ax} {bx}).xls') # excelisim
z, k, m, n, p, t = 0, 0, 0, 0, 0, 0
studentGuvenAlt, aadmGuvenAlt, maadGuvenAlt, madmGuvenAlt, johnsonGuvenAlt, chenGuvenAlt = list(
), list(), list(), list(), list(), list()
studentGuvenUst, aadmGuvenUst, maadGuvenUst, madmGuvenUst, johnsonGuvenUst, chenGuvenUst = list(
), list(), list(), list(), list(), list()