import numpy as np
[docs]
def quantile(sample: np.ndarray, p: float, type: int = 7,
sorted: bool = False, interpolate: bool = True) -> float:
"""
Estimate a desired quantile of a univariate distribution from a vector of samples
Parameters
----------
sample
A 1D vector of values
p
The desired quantile in (0,1)
type
The method for computing the quantile.
See https://wikipedia.org/wiki/Quantile#Estimating_quantiles_from_a_sample
sorted
Whether or not the vector is already sorted into ascending order
interpolate
Whether to interpolate the desired quantile.
Returns
-------
An estimate of the quantile
"""
N = len(sample)
if N == 0:
raise ValueError("Cannot compute quantiles with zero samples.")
if len(sample.shape) != 1:
raise ValueError("Quantile estimation only supports vectors of univariate samples.")
if not 1/N <= p <= (N-1)/N:
raise ValueError(f"The {p}-quantile should not be estimated using only {N} samples.")
sorted_sample = sample if sorted else np.sort(sample)
if type == 6:
h = (N+1)*p
elif type == 7:
h = (N-1)*p + 1
elif type == 8:
h = (N+1/3)*p + 1/3
else:
raise ValueError("type must be an int with value 6, 7 or 8.")
h_floor = int(h)
quantile = sorted_sample[h_floor-1]
if h_floor != h and interpolate:
quantile += (h - h_floor)*(sorted_sample[h_floor]-sorted_sample[h_floor-1])
return float(quantile)