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We propose a mixture model of open clusters (OCs) in the color-magnitudediagrams (CMDs) to measure the OC properties, including isochrone parameters(age, distance, metallicity, and dust extinction), stellar mass function (MF),and binary parameters (binary fraction and mass-ratio distribution), with highprecision and reliability. The model treats an OC in the CMD as a mixture ofsingle and binary member stars and field stars in the same region. The clustermembers are modeled using a theoretical stellar model, MF and binaryproperties. The field component is modeled nonparametrically using a separatefield-star sample in the vicinity of the cluster. Unlike conventional methodsthat rely on stringent member selection, ours allows us to use a sample of morecomplete cluster members and attendant field stars. The larger star samplereduces the statistical error and diminishes the potential bias by retainingmore stars that are crucial for age estimation and MF measurement. Aftervalidating the method with 1000 mock clusters, we measured the parameters of 10real OCs using Gaia EDR3 data. The best-fit isochrones are consistent withprevious measurements in general but with more precise age estimates forseveral OCs. The inferred MF slope is -2.7 to -1.6 for clusters younger than 2Gyr, while older clusters appear to have significantly flatter MFs. The binaryfraction is 30% to 50%. The photometric and astrometric distances agree well.

MiMO: Mixture Model for Open Clusters in Color-Magnitude Diagrams