Which Arkham came first?

I'm curious to delve into the mysteries of the Arkham universe. Could you elaborate on the question, "Which Arkham came first?" I'm referring to the various iterations and interpretations of the infamous Arkham Asylum in both fictional and real-world contexts. Is it the literary predecessor in the works of H.P. Lovecraft, or the iconic Gotham City institution from Batman comics? Perhaps you're referring to the Arkham Horror board game, or even a modern reinterpretation in film or television. Clarifying this query would greatly assist in providing an accurate and comprehensive response.