# What is the analog of the PDF and CDF for the likelihood function?

In probability, we can find the cdf using the pdf and vise-versa. Integrating pdf yields the cdf.

Does integrating the likelihood function yield any important thing?

In statistics, $$\mathcal{L} (M\mid X )= P(X \mid M)$$.

If, cdf is to pdf, then likelihood is to what?

Likelihood integration (with respect to $$M$$) doesn't make sense because it doesn't even integrate/sum to $$1$$ if we iterate over all possible $$M$$'s. However, integration/sum of likelihood multiplied with prior makes sense because the integral is equal to the evidence.
With respect to $$x$$, it's still a density/PMF and its integral is a CDF.