  This paper reviews the Lindley distribution and then introduces the scale and
the double truncation. The unknown parameters of the truncated Lindley
distribution are evaluated with the maximum likelihood estimators. An
application of the Lindley distribution with scale is done to the initial mass
function for stars. The magnitude version of the Lindley distribution with
scale is applied to the luminosity function for the Sloan Digital Sky Survey
(SDSS)
  galaxies and to the photometric maximum of the 2MASS Redshift Survey (2MRS)
galaxies. The truncated Lindley luminosity function allows us to model the
Malquist bias of the 2MRS galaxies.
