Figure 2

Estimating the density of the χ²-distribution. For different degrees of freedom, the true (black line) and the estimated density (red line) of the χ²-distribution are shown, where the density is estimated by applying the procedure of Efron and Tibshirani [19] to 100,000 values randomly drawn from the χ²-distribution. The cyan line marks the estimated density when the inner knots of the natural cubic spline are centered around the median in the df ≥ 3 case.