Use our free Folded Normal Distribution Calculator to quickly determine the Probability Density Function (PDF) and Cumulative Distribution Function (CDF). This tool helps statisticians, engineers, and data scientists analyze the distribution of the absolute value of a normal random variable, simplifying complex statistical computations.
Formula:
The Folded Normal Distribution describes the probability distribution of the absolute value of a normal random variable. If X is a normal random variable with mean μ and standard deviation σ, then Y = |X| follows a folded normal distribution.
This calculator computes the Probability Density Function (PDF) and Cumulative Distribution Function (CDF) for a specific value y.
Where:
y: The non-negative value for which to evaluate the PDF and CDF.μ(mu): The mean of the original (unfolded) normal distribution.σ(sigma): The standard deviation of the original (unfolded) normal distribution (must be > 0).
The PDF is generally given by: (y; μ, σ) = \frac{1}{σ \sqrt{2\pi}} \left[ e^{-\frac{(y-μ)^2}{2σ^2}} + e^{-\frac{(y+μ)^2}{2σ^2}} \right]$ for \ge 0$.
The CDF is generally given by: (y; μ, σ) = \Phi\left(\frac{y-μ}{σ}\right) - \Phi\left(\frac{-y-μ}{σ}\right)$ for \ge 0$, where $\Phi(z)$ is the standard normal CDF.