We analyse a sample of 236 Cepheids from the hipparcos catalog , using the method of “ reduced parallaxes ” in V,I,K and the reddening-free “ Wesenheit-index ” .
We compare our sample to those considered by Feast & Catchpole ( 1997 ) and Lanoix et al .
( 1999 ) , and argue that our sample is the most carefully selected one with respect to completeness , the flagging of overtone pulsators , and the removal of Cepheids that may influence the analyses for various reasons ( double-mode Cepheids , unreliable hipparcos solutions , possible contaminated photometry due to binary companions ) .

From numerical simulations , and confirmed by the observed parallax distribution , we derive a ( vertical ) scale height of Cepheids of 70 pc , as expected for a population of 3-10 M _ { \odot } stars .
This has consequences for Malmquist- and Lutz-Kelker ( Lutz & Kelker 1973 , Oudmaijer et al .
1998 ) type corrections which are smaller for a disk population than for a spherical population .

The V and I data suggest that the slope of the Galactic PL -relations may be shallower than that observed for LMC Cepheids , either for the whole period range , or that there is a break at short periods ( near \log P _ { 0 } \approx 0.7 - 0.8 ) .

We stress the importance of two systematic effects which influence the distance to the LMC : the slopes of the Galactic PL -relations and metallicity corrections .
In order to assess the influence of these various effects , we present 27 distance moduli ( DM ) to the LMC .
These are based on three different colours ( V,I,K ) , three different slopes ( the slope observed for Cepheids in the LMC , a shallower slope predicted from one set of theoretical models , and a steeper slope as derived for Galactic Cepheids from the surface-brightness technique ) , and three different metallicity corrections ( no correction as predicted by one set of theoretical models , one implying larger DM as predicted by another set of theoretical models , and one implying shorter DM based on empirical evidence ) .
We derive DM between 18.45 \pm 0.18 and 18.86 \pm 0.12 .
The DM based on K are shorter than those based on V and I and range from 18.45 \pm 0.18 to 18.62 \pm 0.19 , but the DM in K could be systematically too low by about 0.1 magnitude because of a bias due to the fact that NIR photometry is available only for a limited number of stars .

From the Wesenheit-index we derive a DM of 18.60 \pm 0.11 , assuming the observed slope of LMC Cepheids and no metallicity correction , for want of more information .

The DM to the LMC based on the parallax data can be summarised as follows .
Based on the PL -relation in V and I , and the Wesenheit-index , the DM is

18.60 \pm 0.11 ( \pm 0.08 { slope } ) ( ^ { +0.08 } _ { -0.15 } { metallicity } ) , which is our current best estimate .
Based on the PL -relation in K the DM is 18.52 \pm 0.18

( \pm 0.03 { slope } ) ( \pm 0.06 { metallicity } ) ( ^ { +0.10 } _ { -0 } { sampling% bias } ) . The random error is mostly due to the given accuracy of the hipparcos parallaxes and the number of Cepheids in the respective samples .
The terms between parentheses indicate the possible systematic uncertainties due to the slope of the Galactic PL -relations , the metallicity corrections , and in the K -band , due to the limited number of stars .
Recent work by Sandage et al .
( 1999 ) indicates that the effect of metallicity towards shorter distances may be smaller in V and I than indicated here .

From this , we point out the importance of obtaining NIR photometry for more ( closeby ) Cepheids , as for the moment NIR photometry is only available for 27 % of the total sample .
This would eliminate the possible bias due to the limited number of stars , and would reduce the random error estimate from 0.18 to about 0.10 mag .
Furthermore , the sensitivity of the DM to reddening , metallicity correction and slope are smallest in the K -band .