Among Barndorff-Nielsen's early scientific contributions are his work on exponential families and on the foundations of statistics, in particular sufficiency and conditional inference. In 1977 he introduced the hyperbolic distribution as a mathematical model of the size distribution of sand grains, formalising heuristic ideas proposed by Ralph Alger Bagnold. He also derived the larger class of generalised hyperbolic distributions. These distributions, in particular the normal-inverse Gaussian (NIG) distribution, have later turned out to be useful in many other areas of science, in particular turbulence and finance. The NIG-distribution is now widely used to describe the distribution of returns from financial assets.