  The distributions of trade values and relationships among countries and
product categories reflect how countries select their trade partners and design
export portfolios. Here we consider the exporter-importer network and the
exporter-product network with directed links weighted by the logarithm of the
corresponding export values each year from 1962 to 2018, and study how the
weights of the outgoing links from each country are distributed. Such local
logarithmic export distributions by destinations and products are found to
follow approximately the Gaussian distribution across exporters and time,
implying random assignment of export values on logarithmic scale. However, a
non-zero skewness is identified, changing from positive to negative as
exporters have more partner importers and more product categories in their
portfolios. Seeking the origin, we analyze how local exports depend on the
out-degree of exporter and the in-degrees of destinations/products and
formulate their quantitative and measurable relation incorporating randomness,
which uncovers the fundamental nature of the export strategies of individual
countries.
