Adding a distribution class for the continuous contractual setting

[larryshamalama]

Addresses bullet point 2 in #25.

This PR adds a distribution class for the continuous contractual setting and a corresponding notebook to how to use this distribution. For now, this PR can serve as a discussion platform as I polish the code and add tests.

The distribution class is in fact very similar to #16 with an extra argument to explicitly say if a customer has churned or not at time t_x.

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[ricardoV94]

Still getting biased inference?

Does the original paper have a dataset that we can use to see if recovered parameters are similar? That would help understanding if the bias is in the logp or rng_fn

[larryshamalama]

For now yes, I'll have to dig through the math and the data-generating mechanism to identify the sources of bias.

[ricardoV94]

Can you link the reference paper?

[larryshamalama]

I didn't use one to derive the log-likelihood. The closest paper to my knowledge is the continuous non-contractual setting by Fader, Hardie et Lee (2005)

[ricardoV94]

Have you found out what the EG model in the grid picture is? #25

[larryshamalama]

I think the example being referred to is credit card subscription. To get off the subscription, the cancellation must be explicit (contractual), but the timing of the cancellation can occur anytime (continuous).