def approximate_confidence_interval(x):
a = 1.0*np.array(x)
n = len(a)
m, se = np.mean(a), sem(a)
h = se * norm._ppf((1+0.95)/2)
return m-h, m+h
def get_Z_alpha(confidence):
var = 1 - (1 - confidence) / 2
return norm._ppf(var)
def make_plot_probit(title, input_data, x_label):
'''Creates Probit plot for EUR and data that has a log-normal distribution.
'''
# Calculate log-normal distribtion for input data
sigma, floc, scale = lognorm.fit(input_data, floc=0)
mu = math.log(scale)
x = np.linspace(0.001, np.max(input_data) + np.mean(input_data), 1000)
pdf = 1/(x * sigma * np.sqrt(2*np.pi)) * \
np.exp(-(np.log(x)-mu)**2 / (2*sigma**2))
cdf = (1 + scipy.special.erf((np.log(x) - mu) / (np.sqrt(2) * sigma))) / 2
p = figure(title=title, background_fill_color="#fafafa", x_axis_type='log')
# Prepare input data for plot
input_data_log = np.log(input_data)
# Get percentile of each point by getting rank/len(data)
input_data_log_sorted = np.argsort(input_data_log)
ranks = np.empty_like(input_data_log_sorted)
ranks[input_data_log_sorted] = np.arange(len(input_data_log))
# Add 1 to length of data because norm._ppf(1) is infinite, which will occur for highest ranked value
input_data_log_perc = [(x + 1) / (len(input_data_log_sorted) + 1)
for x in ranks]
input_data_y_values = norm._ppf(input_data_log_perc)
# Prepare fitted line for plot
x_y_values = norm._ppf(cdf)
# Values to display on y axis instead of z values from ppf
y_axis = [1 - x for x in cdf]
# Plot input data values
p.scatter(input_data,
input_data_y_values,
size=15,
line_color="navy",
legend="Input Data",
marker='circle_cross')
p.line(x, x_y_values, line_width=3, line_color="red", legend="Best Fit")
# calculate P90, P50, P10
p10_param = find_nearest(cdf, 0.9)
p10 = round(x[p10_param[1]])
p50_param = find_nearest(cdf, 0.5)
p50 = round(x[p50_param[1]])
p90_param = find_nearest(cdf, 0.1)
p90 = round(x[p90_param[1]])
# Add P90, P50, P10 markers
p.scatter(p90,
norm._ppf(0.10),
size=15,
line_color="black",
fill_color='darkred',
legend=f"P90 = {int(p90)}",
marker='square_x')
p.scatter(p50,
norm._ppf(0.50),
size=15,
line_color="black",
fill_color='blue',
legend=f"P50 = {int(p50)}",
marker='square_x')
p.scatter(p10,
norm._ppf(0.90),
size=15,
line_color="black",
fill_color='red',
legend=f"P10 = {int(p10)}",
marker='square_x')
# Add P90, P50, P10 segments
# p.segment(1, norm._ppf(0.10), np.max(x), norm._ppf(0.10), line_dash='dashed', line_width=2, line_color='black', legend="P90")
# p.segment(1, norm._ppf(0.50), np.max(x), norm._ppf(0.50), line_dash='dashed', line_width=2, line_color='black', legend="P50")
# p.segment(1, norm._ppf(0.90), np.max(x), norm._ppf(0.90), line_dash='dashed', line_width=2, line_color='black', legend="P10")
p.segment(p90,
-4,
p90,
np.max(x_y_values),
line_dash='dashed',
line_width=2,
line_color='darkred',
legend=f"P90 = {int(p90)}")
p.segment(p50,
-4,
p50,
np.max(x_y_values),
line_dash='dashed',
line_width=2,
line_color='blue',
legend=f"P50 = {int(p50)}")
p.segment(p10,
-4,
p10,
np.max(x_y_values),
line_dash='dashed',
line_width=2,
line_color='red',
legend=f"P10 = {int(p10)}")
# Find min for x axis
x_min = int(np.log10(np.min(input_data)))
power_of_10 = 10**(x_min)
# Plot Styling
p.x_range.start = power_of_10
p.y_range.start = -3
p.legend.location = "top_left"
p.legend.background_fill_color = "#fefefe"
p.xaxis.axis_label = x_label
p.yaxis.axis_label = 'Z'
p.left[0].formatter.use_scientific = False
p.xaxis[0].formatter = NumeralTickFormatter(format="0,0")
p.yaxis.visible = False
p.title.text = title
p.title.align = 'center'
p.legend.click_policy = "hide"
return p
def _solve_power_for_pct(self, pct):
z = norm._ppf(pct)
error = lambda est: self._compute_stouffer_z_at_power(est) - z
return opt.brentq(error, .0501, .9999)
def _compute_stouffer_z(pp):
isnotnan = ~np.isnan(pp)
pp_notnan = pp[isnotnan]
return np.sum(norm._ppf(pp_notnan)) / np.sqrt(isnotnan.sum())
def gaussian_icdf(h, Xi, x):
return Xi + h**2 * norm._ppf(x)