Inputs
Results
Enter values and press Compute to see results.
Formulas
PDF: f(x) = (1 / (2 b)) · exp( −|x − μ| / b )
CDF:
if x < μ: F(x) = 0.5 · exp( (x − μ) / b )
if x ≥ μ: F(x) = 1 − 0.5 · exp( −(x − μ) / b )
Standardize: z = (x − μ) / b
Tips
- Use a positive scale b; smaller b produces heavier peak and thinner tails.
- F(x) gives left‑tail probability; 1−F(x) is right‑tail.
- At x = μ, F(x) = 0.5 exactly.
Quick examples
Click an example to auto‑fill inputs; press Compute to update.
FAQs
It controls dispersion. Larger b spreads the distribution and increases tail probabilities; smaller b concentrates mass near μ and decreases tail probabilities.
Yes. F(x) is continuous and equals 0.5 at x = μ, even though the PDF has a cusp there due to the absolute value in the exponent.
The left‑tail probability is F(x). The right‑tail probability is 1 − F(x), also called the survival function. They always sum to 1.
Yes. For |X − μ| ≥ t, compute both tails as F(μ − t) + (1 − F(μ + t)). This tool provides F(x) and 1 − F(x) so you can combine them as needed.
Use any consistent units. x and μ must share the same units; b uses the same units as well. Probabilities are unitless.