Introduction

If you want Gaussian-like random values that are always positive, the first question is what distribution you actually need. A true normal distribution extends across all real numbers, so it cannot be strictly positive. In practice, people usually mean either a truncated normal distribution or a different positive-only distribution such as log-normal or half-normal.

Decide What "Positive Gaussian" Means

There are three common interpretations:

• normal distribution, but reject or truncate negative samples
• half-normal distribution, which reflects negative values to positive ones
• log-normal distribution, which is always positive but not symmetric

These are not interchangeable. If the mean and variance of the original normal distribution matter, truncation is usually the closest fit. If you only need positive skewed values, log-normal may be more natural.

Simple Rejection Sampling in Pure Python

The most direct method is to sample from a normal distribution and keep only positive values.

1import random
2
3
4def positive_normal(mu=10.0, sigma=2.0):
5    while True:
6        x = random.gauss(mu, sigma)
7        if x > 0:
8            return x
9
10samples = [positive_normal() for _ in range(5)]
11print(samples)

This is easy to understand and works well when the mean is far enough above zero that negative samples are rare. It becomes inefficient if the original normal distribution produces many negatives.

Use a Truncated Normal Distribution with SciPy

If you want a principled positive-only version of a normal distribution, SciPy's truncated normal is usually the best answer.

1import numpy as np
2from scipy.stats import truncnorm
3
4mu = 10.0
5sigma = 2.0
6lower = 0.0
7upper = np.inf
8
9a = (lower - mu) / sigma
10b = (20.0 - mu) / sigma  # example finite upper bound
11
12samples = truncnorm.rvs(a, b, loc=mu, scale=sigma, size=10)
13print(samples)

If you truly want no upper bound, use a large practical bound or another supported approach depending on your library version. The important point is that the distribution is explicitly truncated rather than only filtered afterward.

Half-Normal and Log-Normal Alternatives

If you only need positive values and do not need the result to behave like a clipped normal around a chosen mean, other distributions may be better.

Half-normal from the absolute value of a zero-mean normal:

1import numpy as np
2
3samples = np.abs(np.random.normal(loc=0.0, scale=2.0, size=10))
4print(samples)

Log-normal:

1import numpy as np
2
3samples = np.random.lognormal(mean=1.0, sigma=0.3, size=10)
4print(samples)

These are always positive, but they do not have the same interpretation as a normal distribution truncated at zero.

Parameter Choices Matter

When you move from an unconstrained normal distribution to a positive-only version, the mean and spread of the resulting samples change. That means you should validate the generated sample statistics instead of assuming the original mu and sigma still describe the final output directly. This matters a lot in simulation and synthetic-data workflows.

Common Pitfalls

• Asking for a positive normal distribution as if that were still a standard Gaussian.
• Using absolute value when the intended model is actually truncation.
• Ignoring efficiency when rejection sampling discards a large fraction of values.
• Comparing means and standard deviations without accounting for how truncation changes them.
• Choosing log-normal because it is positive without checking whether the skewed shape matches the problem.

Summary

• A true Gaussian cannot contain only positive values.
• The most common practical answer is a truncated normal distribution.
• Rejection sampling is simple when negative values are rare.
• Half-normal and log-normal are useful alternatives, but they represent different statistical assumptions.
• Choose the distribution based on the modeling goal, not only on the positivity constraint.