Chi-Squared Distribution
Used to test if data fits a model (goodness of fit) or if variables are independent.
Probability Density FunctionPDF = f(x)
Cumulative Distribution FunctionCDF = F(x)
Probability in an Interval
Compute the probability that X falls between two values. For continuous distributions, this is the shaded area under the PDF (≤ vs < doesn't matter).
P(a ≤ X ≤ b)
Quantiles (Inverse CDF)
Pick a probability p and read the corresponding quantile xₚ where F(xₚ) = p.
Quantile xₚ (where F(xₚ) = p)
In Chi-Squared Distribution, selected probability p: 0.9500 (95.00%)
Parameters
Adjust the parameters and (optionally) add up to 3 curves to compare different settings side‑by‑side.
0 curves shown
Estimating parameters from data
If you’re fitting this distribution to observed data, these are common plug‑in estimates you can start with.
Degrees of Freedom (k)
Typically relates to the number of independent variables or sample size minus constraints.