"A two dimensional data samples for probability density function estimation"

"The data points are generated by sampling from the ground-truth probability density function defined as f(\\boldsymbol{x})=0.45\\mathcal{N}({{x}_{1}}|{{\\mu }_{0}},{{(\\beta {{x}_{2}})}^{-1}}\\Gamma ({{x}_{2}}|a,b)+0.2\\mathcal{N}(\\boldsymbol{x}|{{\\boldsymbol{\\mu} }_{1}},{{\\boldsymbol{\\Sigma} }_{1}})+0.35\\mathcal{N}(\\boldsymbol{x}|{{\\boldsymbol{\\mu} }_{2}},{{\\boldsymbol{\\Sigma}}_{2}}) , where {{\\mu }_{0}}=5,\\beta=a=b=2,{{\\boldsymbol{\\mu} }_{1}}={{(5,5)}^{T}},{{\\boldsymbol{\\mu} }_{2}}={{(5.5,4.6)}^{T}}. The constructed synthetic dataset is employed to quantitatively evaluate and compare the performance of various probability density estimation methods, including both parametric and nonparametric approaches. By using such a controllable and analytically known true distribution, we are able to reliably measure the accuracy, stability, and effectiveness of the tested density estimation algorithms under controlled experimental conditions."