Solomon Kullback was born in 1903.

Solomon Kullback died on 1994-08-05.

Although it is often intuited as a distance metric, the KL divergence is not a true metric, as the Kullback-Leibler divergence is not symmetric, nor does it satisfy the triangle inequality.

The KLD is more or less a measure of how much information is lost when an approximation is used to replace an actual probability distribution.

How you calculate it depends on whether you are considering discrete or continuous values for the distribution.

If you have discrete values,

KLD = Σ P(i) log [P(i)/Q(i)] (summing over the values of i)

where P(i) is the "true" distribution and Q(i) a corresponding approximation.

If you have a continuous function for the probability, i.e. the variable can assume any value over a certain range (usually with different probability density for different values since uniform probability is a pretty boring problem)

KLD = ∫ p(x)log[p(x)/q(x)] dx (integrated from -∞ to +∞)

where p(x) is the true function of the probability - the "density" of P, and q(x) is the approximated function of the probability - the "density" of Q.

Note that these formulas only hold for a single variable. More complex formulas are required to calculate the KLD for multi-variable distributions.

Robert J. Allan is a naval architect known for his expertise in ship design, particularly in the field of tugboats and icebreakers. He has authored numerous technical papers and books on marine engineering and ship design, focusing on innovative and efficient vessel designs. Allan's work has had a significant impact on the maritime industry, with many of his designs being widely used around the world.