import numpy as np
import pandas as pd
[docs]
def dnorm(x, mean=0, sd=1):
"""
Calculates the Probability Density of the normal distribution at a given point.
Parameters
----------
x : float
The point at which to evaluate the PDF.
mean : float, optional
The mean (average) of the normal distribution. Default is 0.
sd : float, optional
The standard deviation of the normal distribution. Default is 1.
Returns
-------
result_df : pandas.DataFrame
A DataFrame containing the input value and the corresponding PDF value.
Raises
------
ValueError
If `sd` is zero or negative, as the standard deviation must be a positive number.
TypeError
If any of the input parameters (`x`, `mean`, `sd`) are not numerical.
Example
-------
>>> dnorm(1.96, mean=0, sd=1)
x PDF
0 1.96 0.058440
>>> result_df = dnorm(1.96, mean=0, sd=1)
>>> result_df
x PDF
0 1.96 0.058440
"""
# Input type checks
if not isinstance(x, (float, int)):
raise TypeError(f"Expected `x` to be float or int, got {type(x)}")
if not isinstance(mean, (float, int)):
raise TypeError(f"Expected `mean` to be float or int, got {type(mean)}")
if not isinstance(sd, (float, int)):
raise TypeError(f"Expected `sd` to be float or int, got {type(sd)}")
# Value checks
if sd <= 0:
raise ValueError("Standard deviation `sd` must be positive.")
# Calculate the PDF value
pdf = (1 / (sd * np.sqrt(2 * np.pi))) * np.exp(-0.5 * ((x - mean) / sd) ** 2)
# Create a DataFrame with the results
result_df = pd.DataFrame({
"x": [x],
"PDF": [pdf]
})
return result_df