On iOS, if you're wanting to distribute the entire application from your website without using the App Store it's not possible as a general rule. The two exceptions being:
If you get an Enterprise developer's account from Apple, then you can prepare installation packages that will work from a web site. However, you may only distribute the application to direct employees.
For testing stages you can prepare ad-hoc releases and then work with a company such as TestFlight. If you take this approach you're limited to release to 100 devices per year and each release is only valid for 3 months. You can't remove devices from the list except on the anniversary date of your developer account.
If you're actually wanting to put the installer application in the App Store and then download the actual Application, it's not allowed under any circumstances. The ToS prohibit you from having an application which downloads executable code or script (with the implicit exception of a web application)