1 Introduction

Long period variables (LPV) form an important class of red giant stars. They show more or less regular photometric variability with amplitudes reaching up to 8 mag and periods up to 600 days. They traditionally comprise Miras, semi-regular (SR) and irregular (L) variables according to the amplitude and the regularity of their visual light curves. They are known to be either O-rich or C-rich, and comprise thus M, S and C stars. More recently OH-IR sources have been found from infrared and radio observations showing that they belong to the LPV population with periods up to 2000 days. Those sources emit in the infrared and radio wavelengths, and are not associated with any detectable counterpart in optical wavelengths.

The brightest LPVs are luminous enough to be observed at long distances, providing information on the host galaxy, like the Magellanic Clouds (see Van Loon et al. 1999 as an example). While the ranges of masses and ages of LPVs are still the subject of discussion, it is generally accepted that they are large, and are therefore considered as very good tracers of galactic history.

The determination of the characteristics of individual LPVs is usually a delicate task due to the complexity of the dynamic and chemical phenomena to be considered. A statistical study using all available data of a large sample of LPVs is often needed. A rough example of such an approach could be the relation between the mean visual light curves and the infrared colors of C and O-rich LPVs already presented in Mennessier et al. (1997a). In this paper, HIPPARCOS astrometric data and the available multi-wavelength (K, IRAS 12 and 25) infrared photometric measurements allow us to calibrate multi-wavelength luminosities and to discriminate between different galactic populations - and thus different ranges of initial masses ( ${\cal M}_{\rm ms}$) - among the LPVs according to their kinematical properties. In a second step, individual K and IRAS absolute magnitudes are estimated for all the 800 considered LPVs using a powerful statistical estimator.

Our sample of LPV stars and the data used are described in Sect. 2. The statistical method specifically developed for the study of HIPPARCOS samples is summarized in Sect. 3. Section 4 presents the discriminated groups of LPVs resulting from our statistical analysis, while Sect. 5 analyzes the results derived for individual stars. Finally, Sect. 6 reviews the crossed properties derived from the analysis at different wavelengths.