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=== Fitting to data ===
The coefficients <math>\boldsymbol a</math> can be determined from data by [[linear least squares]]. Given <math>m</math> data points <math>(x_i,y_i)</math> that are intended to characterize the CDF of a QPD, and <math>m \times n</math> matrix <math>\boldsymbol Y</math> whose elements consist of <math>g_j (y_i)</math>, then, so long as <math>\boldsymbol Y^T \boldsymbol Y</math> is invertible, coefficients' column vector <math>\boldsymbol a</math> can be determined as <math>\boldsymbol a=(\boldsymbol Y^T \boldsymbol Y)^{-1} \boldsymbol Y^T \boldsymbol x</math>, where <math>m\geq n</math> and column vector <math>\boldsymbol x=(x_1,\ldots,x_m)</math>. If <math>m=n</math>, this equation reduces to <math>\boldsymbol a=\boldsymbol Y^{-1} \boldsymbol x</math>, where the resulting CDF runs through all data points exactly. An alternate method, implemented as a linear program, determines the coefficients by minimizing the sum of absolute distances between the CDF and the data subject to feasibility constraints.<ref name="Faber">
=== Shape flexibility ===
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