Master Compression and Clipping Analysis
In this post I want to analyze clipping and compression by looking at songs that are plotted as a histogram of the normalized amplitudes of the song waveform. Normalized meaning the maximum song waveform value is 1 and the minimum is -1. The x-axis is the amplitude of the audio signal and the y-axis is the number of samples at that amplitude.
Relatively Uncompressed and Unclipped
Before we dive in let's look at a song that is relatively uncompressed and unclipped

Above is a standard looking song that doesn't appear to have much compression or clipping. Compare this with the images below
Compression and a Little Clipping

This is a histogram of the deadmau5 song "I Remember". You can see the spikes at the top of the histogram, which represent clipping. It also moves out linearly like a pyramid, which I believe implies the linear compression ratio being applied beyond the threshold.
Compression and Heavy Clipping

The image above is a histogram of the skrillex song "Scary Monsters and Nice Sprites". You can see the outsized spikes at the top of the histogram, which represent clipping.