For example, Beat Cepheids and Beat RR Lyrae oscillate at more than one frequency. . Different classes of variable stars can be located in different regions of a plot of magnitude versus temperature or spectral type. Different types of variable curves are classified also on the basis of the shapes of their light curves and the relationships of shapes to period, for example. As well as being important for studies of stellar structure and evolution, these classes are used to determine distances on a cosmic scale by means of the relationship of their periods to their magnitudes. Observations of these stars are typically made at rather irregular times, depending on observation schedules and sky conditions.
Different observations have differing errors.
All this makes determination of the periods and the shapes of the corresponding phased light curves an interesting statistical problem. The basic idea is that the adequacy of a candidate period is judged by the magnitude of the variation about a smooth curve passed through the data folded at that period.