Canonly, in the Horatio Hornblower Series, the Earl of Edrington is only a Major. However, five years have since passed, and by no means would he have simply stayed a Major in these five years. Oh no. To keep him at the same point, canon-wise, to his canon mates, and to keep his progression in rank accordingly with the number of years passed, I (with a bit of help) devised this timeline:
1774- Born Alexander Lauder to his parents, Robert and Annabella Lauder
1789- Ensign, joining the army at the age of 15.
1792- Captain of his first company. Age 18.
1795- Major at age 21.
1797- (Frogs and Lobsters) Age 23.
1798- Lieutenant Colonel at 24.
1802- Colonel at 28.
1805- Arrival to Bell Pointe, having been en route to receive promotion for Brigadier. Age 31.
Most of this timeline is based off of the man Edrington is most likely modeled after, as there was, historically, no Earl of Edrington at the time of the series. While there was, at some point, some several centuries earlier, an Earl of Edrington, I was forced to mash a bit of history in order to make it work.
Therefore, the names of the family are taken from the actual family who had the Edrington Estate, the Lauder family. His achievements, historical battles, and his 'canon' history is taken from Sir William Stewart, the British army officer who lead the forces at Quiberon.
While it may seem like a coincidental choice to select Sir William Stewart as the model for who Edrington is based off of, I present the Cumloden Papers as evidence to the contrary. Viscount Horatio Nelson, the confirmed man after which Horatio Hornblower is based off of, was a Naval Captain with whom Stewart served with, aboard Nelson's own ship. They not only knew each other, but wrote letters, half of the correspondence published in the Cumloden Papers. Additionally, it is stated in the film that Edrington is the Major of the 95th foot, Stewart's creation that later became the 95th Rifle Corps.
Additional sources for research:
Excerpt on Sir William Stewart from Oxford Dictionary of National Biography
Wikipedia article on Robert Lauder, Earl of Edrington
Napoleonic Guide - Armies of the war
The Life of a Regiment: Gardyne, C. G. From its formation in 1794 to 1816
... STILL IN PROGRESS