How can I change the purple background color of Ubuntu plymouth boot screen?

It's pretty easy.

Open the file /lib/plymouth/themes/ubuntu-logo/ubuntu-logo.script with an editor and change the following 2 lines that can be found to something like this

Window.SetBackgroundTopColor (0.0, 0.00, 0.0);     # Nice colour on top of the screen fading to
Window.SetBackgroundBottomColor (0.0, 0.00, 0.0);  # an equally nice colour on the bottom

save the file and run the following command.

sudo update-initramfs -u

The background of the boot splash should now be black instead of purple.

Note that in Ubuntu 16.04, the themes directory location changed to /usr/share/plymouth/themes.

The path location has changed since Ubuntu 16.04. See below

To open the file:

sudo nano /usr/share/plymouth/themes/ubuntu-logo/ubuntu-logo.script

Then as before, edit these two rows:

Window.SetBackgroundTopColor (0.0, 0.00, 0.0);     # Nice colour on top of the screen fading to
Window.SetBackgroundBottomColor (0.0, 0.00, 0.0);  # an equally nice colour on the bottom

And run:

sudo update-initramfs -u