The
statistical relationship between human height and weight is of especial
importance to clinical medicine, epidemiology, and the biology of human
development. Yet, after more than a century of anthropometric measurements and
analyses, there has been no consensus on this relationship. The purpose of this
article is to provide a definitive statistical distribution function from which
all desired statistics (probabilities, moments, and correlation functions) can
be determined. The statistical analysis reported in this article provides
strong evidence that height and weight in a diverse population of healthy
adults constitute correlated bivariate lognormal random variables. This
conclusion is supported by a battery of independent tests comparing empirical
values of 1) probability density patterns, 2) linear and higher order
correlation coefficients, 3) statistical and hyperstatistics moments up to 6th order, and 4) distance
correlation (dCor) values to corresponding theoretical quantities: 1) predicted
by the lognormal distribution and 2) simulated by use of appropriate random
number generators. Furthermore, calculation of the conditional expectation of
weight, given height, yields a theoretical power law that specifies conditions
under which body mass index (BMI) can be a valid proxy of obesity. The
consistency of the empirical data from a large, diverse anthropometric survey
partitioned by gender with the predictions of a correlated bivariate lognormal
distribution was found to be so extensive and close as to suggest that this outcome is not coincidental or
approximate, but may be a consequence of some underlying biophysical mechanism.
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