{ { JHK _ { \mathrm { s } } } } magnitudes corrected to mean intensity are estimated for LMC type II Cepheids in the OGLE-III survey .
Period-luminosity ( PL ) relations are derived in { JHK _ { \mathrm { s } } } as well as in a reddening-free VI parameter .
Within the uncertainties the BL Her stars ( P < 4 d ) and the W Vir stars ( P = 4 to 20 d ) are co-linear in these PL relations .
The slopes of the infrared relations agree with those found previously for type II Cepheids in globular clusters within the uncertainties .
Using the pulsation parallaxes of V553 Cen and SW Tau the data lead to an LMC modulus uncorrected for any metallicity effects of 18.46 \pm 0.10 mag .
The type II Cepheids in the second-parameter globular cluster , NGC 6441 , show a PL ( VI ) relation of the same slope as that in the LMC and this leads to a cluster distance modulus of 15.46 \pm 0.11 mag , confirming the hypothesis that the RR Lyrae variables in this cluster are overluminous for their metallicity .
It is suggested that the Galactic variable \kappa Pav is a member of the peculiar W Vir class found by the OGLE-III group in the LMC .
Low-resolution spectra of OGLE-III type II Cepheids with P > 20 d ( RV Tau stars ) show that a high proportion have TiO bands ; only one has been found showing C _ { 2 } .
The LMC RV Tau stars , as a group , are not co-linear with the shorter-period type II Cepheids in the infrared PL relations in marked contrast to such stars in globular clusters .
Other differences between LMC , globular cluster and Galactic field type II Cepheids are noted in period distribution and infrared colours .