def random_normal(*dims: int,
mean: float = 0.0,
variance: float = 1.0) -> Tensor:
if len(dims) == 1:
return [
mean + variance * inverse_normal_cdf(random.random())
for _ in range(dims[0])
]
else:
return [
random_normal(*dims[1:], mean=mean, variance=variance)
for _ in range(dims[0])
]
def random_normal() -> float:
# Returns a random draw from a standard normal distribution
return inverse_normal_cdf(random.random())
##############################################################################################################
"""
# Data
import random
from Probability import inverse_normal_cdf
random.seed(0)
# Data 1
#uniform between -100 and 100
uniform = [200 * random.random() - 100 for _ in range(10000)]
#Data 2
#normal distrinution with mean 0, standard deviation 57
normal = [57 * inverse_normal_cdf(random.random()) for _ in range(10000)]
# Plot Data 1
plot_histogram(uniform, 10, "Uniform Histogram")
# Plot Data 2
plot_histogram(normal, 10, "Normal Histogram")
"""
##############################################################################################################
########################## 2-dimensional data ##########################
##############################################################################################################
"""
def random_normal() -> float:
# Returns a random draw from a standard normal distribution
return inverse_normal_cdf(random.random())
def normal_lower_bound(probability: float,
mu: float = 0,
sigma: float = 1) -> float:
"""Returns the z for which P(Z >= z) = probability"""
return inverse_normal_cdf(1 - probability, mu, sigma)
def normal_upper_bound(probability:float,
mu:float = 0,
sigma: float = 1)-> float:
# Returns the z for which P(Z<=z) = probability
return inverse_normal_cdf(probability, mu, sigma)
def normal_lower_bound(probability, mu=0, sigma=1): """return the z for which P(Z >= z) = probability""" return inverse_normal_cdf(1 - probability, mu, sigma)
def normal_upper_bound(probability, mu=0, sigma=1): """returns the z for which P(Z <= z) = probability""" return inverse_normal_cdf(probability, mu, sigma)