Figure 8.

Kernel density estimation for the distribution of the pulmonary arterial flow fraction (γ) in (a) malignant pleural mesothelioma (MPM) and (b) nonsmall cell lung cancer (NSCLC). The distribution of $\gamma$ values derived from the Tofts‐Kety (TK), two compartment exchange (2CX), adiabatic approximation to the tissue homogeneity (AATH), and distributed parameter (DP) models except for the extended TK (ETK) model tended to be left‐skewed in both types of tumors. The basic kernel estimator can be expressed as ${\widehat{f}}_{\mathit{kde}}\left(x\right)=\frac{1}{n}\sum _{i=1}^{n}K\left(\frac{x-x_i}{h}\right)$ , where n refers to independent observations x₁, x₂, …, x_n from the random variable X, K(·) is the kernel function and h is the bandwidth. In this study, a Gaussian kernel with a random variable X = γ and a bandwidth h = 3 was used to produce smooth estimate.