Multi-color light curves and radial velocities for TYC 1031 1262 1 have been obtained and analyzed .
TYC 1031 1262 1 includes a Cepheid with a period of 4.15270 \pm 0.00061 days .
The orbital period of the system is about 51.2857 \pm 0.0174 days .
The pulsation period indicates a secular period increase with an amount of 2.46 \pm 0.54 min/yr .
The observed B , V , and R magnitudes were cleaned for the intrinsic variations of the primary star .
The remaining light curves , consisting of eclipses and proximity effects , are obtained and analyzed for orbital parameters .
The system consists of two evolved stars , F8II+G6II , with masses of M _ { 1 } =1.640 \pm 0.151 { M } _ { \odot } and M _ { 2 } =0.934 \pm 0.109 { M } _ { \odot } and radii of R _ { 1 } =26.9 \pm 0.9 { R } _ { \odot } and R _ { 2 } =15.0 \pm 0.7 { R } _ { \odot } .
The pulsating star is almost filling its corresponding Roche lobe which indicates the possibility of mass loss or transfer having taken place .
We find an average distance of d=5070 \pm 250 pc using the BVR and JHK magnitudes and also the V-band extinction .
Kinematic properties and the distance to the galactic plane with an amount of 970 pc indicate that it belongs to the thick-disk population .
Most of the observed and calculated parameters of the TYC 1031 1262 1 lead to a classification of an Anomalous Cepheid .