Kig-Yar Major

Jackal Major is an elevated rank for more experienced Jackals of the Covenant. They are characterized by their orange shields, and usually wear armor that is beige or brown in color, though this is not always the case. They are seen commanding Jackal Minors or Grunts in combat. Their shields become gradually red as they weaken in strength.

In Halo 3, their shields appear to be light purple.

Combat
Jackal Majors almost always wield Plasma Pistols which they are fond of overcharging. Be very careful when attacking them from the front. These Jackals are trickier than their less experienced counterparts. They are better at blocking themselves with their shields, and can usually roll out of the way of a Frag Grenade. The best way to kill them is to Melee them, or use a M6C Magnum and land a headshot for an instant kill. This will also work with the Covenant Carbine or the BR55 Battle Rifle as well, or alternatively using a Sniper Rifle to kill them from afar.

Like Minor Jackals, Major Jackals are not tough and should be taken down at your own pace, They are so rarely found alone though, often lead by Lances of Grunts...

Appearances
They appear in almost every level in Halo: Combat Evolved, Halo 2 and Halo 3, with a few exceptions, such as The Library in Halo: CE or The Oracle (Level) in Halo 2.

Halo 3
Though they are not listed in the Bungie.net stats, Jackal Majors are likely in Halo 3 as the violet shield bearing Jackals. On Legendary, these are more common then their blue shielded counterparts, and with Thunderstorm active violet shielded Jackals are the only shield color that appear.

Speculation
It is speculated that Jackal Majors are simply Jackal Snipers that opt to swap their sniping weapons for a purple shield and smaller weapon. That would explain why it is not listed at Bungie.net stats. The character J-011-422 supports this theory. It is possible that Bungie came up with that character to explain why the Jackal Major is not listed on Bungie player stats.

Trivia

 * In Halo: Combat Evolved, the shield colour is the same as a Minor Jackal's