import numpy as np
from scipy.special import erf
[docs]
def pnorm(q, mean=0, sd=1, lower_tail=True):
"""
This function returns the value of the cumulative density function (cdf) of the
normal distribution with mean equal to `mean`, standard deviation equal to `sd`,
at a certain quantile q.
Parameters
----------
q : np.float64
The quantile for which you want the `cdf` value.
mean : np.float64, optional
The mean value of the normal distribution. Default is 0.
sd : np.float64, optional
The standard deviation of the normal distribution. Default is 1.
lower_tail : bool, optional
If True, probabilities are P(X < q), otherwise, P(X > q). Default is True.
Returns
-------
np.float64
A probability value at the given quantile value of the specified cdf.
Examples
-------
>>> pnorm(69, mean=60, sd=5, lower_tail=False)
0.03593032
"""
# Input type checks
if not all(isinstance(param, (int, float)) for param in [q, mean, sd]):
raise TypeError(f"Input parameters must be numerical")
if not isinstance(lower_tail, bool):
raise TypeError(f"Expected variable lower_tail to be boolean, got {type(lower_tail)}")
# Value checks
if sd <= 0:
raise ValueError("Standard deviation must be positive")
if lower_tail:
result = 1/2 * (1 + erf((q-mean)/(np.sqrt(2)*sd)))
return result
else:
result = 1 - 1/2 * (1 + erf((q-mean)/(np.sqrt(2)*sd)))
return result