  Undernutrition, resulting in restricted growth, and quantified here using
height-for-age z-scores, is an important contributor to childhood morbidity and
mortality. Since all levels of mild, moderate and severe undernutrition are of
clinical and public health importance, it is of interest to estimate the shape
of the z-scores' distributions.
  We present a finite normal mixture model that uses data on 4.3 million
children to make annual country-specific estimates of these distributions for
under-5-year-old children in the world's 141 low- and middle-income countries
between 1985 and 2011. We incorporate both individual-level data when
available, as well as aggregated summary statistics from studies whose
individual-level data could not be obtained. We place a hierarchical Bayesian
probit stick-breaking model on the mixture weights. The model allows for
nonlinear changes in time, and it borrows strength in time, in covariates, and
within and across regional country clusters to make estimates where data are
uncertain, sparse, or missing.
  This work addresses three important problems that often arise in the fields
of public health surveillance and global health monitoring. First, data are
always incomplete. Second, different data sources commonly use different
reporting metrics. Last, distributions, and especially their tails, are often
of substantive interest.
