I feel this is a relatively easy question to answer, which makes me doubt whether or not I can provide the answer you are looking for but I will try. Tiberius was a strong general who had a distaste for ruling. He relied on the people left by Augustus, particularly Sejanus, and his close family, particularly his son Drusus, to help control his regime. Whether Sejanus was power hungry, or Tiberius was just paranoid, is up for debate: the result is clear, though. Tiberius began exiling any one close enough to threaten his rule, all while taking longer and longer vacations in Campania and, later, Capri. He relied increasingly on Sejanus as Drusus died and anyone close to his cabal of power was exiled to the furthest limits of the empire. His rule was largely dominated by relatives and persons of power dying under mysterious circumstances, which was a consistent pattern under his mother Livia (Augustus' wife) and probably was inspired by her.

Tiberius spent the majority of his rule in absentia, having lavish parties at his palace in Capri which also had an unusually large number of "mysterious" deaths (Tiberius himself was said to drunkenly push guests over the edge of his deck, overlooking a large cliff which would result in sure death). Anyway, let me include the grain of salt myself. Everything I've said here is sourced from Suetonius or Tacitus (with an emphasis on Suetonius), who are both suspected of heavy favoritism and propaganda against any "bad" emperor, such as Tiberius (again, emphasis on Suetonius).

Sources Tacitus, The Annals.

Suetonius, The Twelve Caesars