Clark Stevenson (@clark-stevenson) has done some great work in cleaning up and modernizing this definition file, so the best place to look for a PIXI TypeScript definitions is in the official Phaser.io repo:
https://github.com/photonstorm/phaser/blob/master/typescript/pixi.d.ts
(permalink https://github.com/photonstorm/phaser/blob/a67d2df6f04a5ede81b51f838b0d6e6dddabe9ba/typescript/pixi.d.ts)
Thanks to all who've filed bugs and submitted pull requests!