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Dwarf spheroidal galaxies (dSphs) are promising targets of indirect detectionexperiments searching for dark matter (DM) at present universe. Toward robustprediction for the amount of signal flux originating in DM annihilation insidedSphs, a precise determination of DM distributions as well as $J$-factors ofthe dSphs is particularly important. In this work, we estimate those of Draco,Sculptor, and Ursa Minor dSphs by an improved statistical method in which bothforeground stars and dSph member stars are simultaneously taken into account.We define the likelihood function of the method as the so-called conditionalone to remove sampling bias of observed stellar data. This improved methodenables us to estimate DM distributions and $J$-factors of the dSphs directlyfrom observed stellar data contaminated by foreground stars without imposingstringent membership criteria on the measured quantities.

$J$-factor estimation of Draco, Sculptor and Ursa Minor dwarf spheroidal galaxies with the member/foreground mixture model