Incorporate input modelling functionality

[amyheather]

Clear, understandable for practitioners.

Works easily with sim-tools, giving sim-tools parameters needed.

https://github.com/ambmodels/ambdes/blob/main/src/ambdes/input_modelling.py

[amyheather]

@TomMonks

Using the code I have for ambdes, I can easily add a fit method to distributions as a classmethod, for the non-combination continuous distributions.

For example, in Exponential:

    @classmethod
    def fit(
        cls,
        data: ArrayLike,
        random_seed: int | SeedSequence | None = None
    ):
        """
        Create an exponential distribution by fitting to observed data.

        Parameters
        ----------
        data : ArrayLike
            Observed data to fit distribution to.
        random_seed : Optional[Union[int, SeedSequence]], default=None
            A random seed or SeedSequence to reproduce samples. If None, a
            unique sample sequence is generated.

        Returns
        -------
        Exponential
            A new instance initialised with the fitted parameters.
        """
        data = np.asarray(data, dtype=np.float64)
        mean = np.mean(data)
        return cls(mean=mean, random_seed=random_seed)

This would then mean you can use exponential like:

exp = Exponential.fit(data)
exp

> Exponential(mean=4955.7404)

exp.sample()

> 410.4170433464011

I can then also add a module with some simple function/s / class/es that can be used to check how good a fit it is.

e.g., Two-sample KS statistic. Two-sample Q-Q plot. Overlaid histograms.

If that sounds good?

PS. I guess can also have fit for discrete? A bit different, but just takes the provided data, turns it into proportions of each unique value.

[amyheather]

BTW. Turns out fitting PearsonV and PearsonVI was easy with scipy when I read your docstrings and realised they had other names.

Unfortunately, I've hit a dead-end fitting to a hyperexponential distribution - or at least, not found a way in Python - might require doing it manually...

[TomMonks]

@amyheather yes this looks great! Very useful

Also great news on PearsonV and VI - glad I included some notes! Also written before GenAI, but sadly I couldn't remember that!

Took a quick peak at the code. For any matplotlib function I recommend returning fig and ax to the calling code as it allows the user to customise the chart. Another useful feature would be to allow a user to pass in ax which means they can add the plot to a custom layout they have created themselves (e.g. a grid).

[amyheather]

• Add fit method to distribution classes.
• Add tests for new fit methods.
• Add input modelling module with code for evaluating distributions.
• Add tests for new input modelling module.
• Add page to documentation explaining how to do input modelling using the new functions.

[amyheather]

Some notes from implementing fit method in distribution classes in 87869e7...

Quirks in implementation:

• Erlang - sim-tools Erlang accepts location, but here, have just fit using mean and stdev. Have not derived location.
• Beta - fit with scipy.stats which also returns loc and scale. sim-tools Beta doesn't accept those, so they are forced to 0 and 1, with data normalised between 0 and 1.
• PearsonV and PearsonVI - these are fit with scipy.stats which also return loc but the sim-tools classes don't support a location parameter, so these are run with floc=0 in scipy.stats to prevent loc parameter.
• Gamma, Weibull and Beta - will fail (inelegantly?) if 0s are present.
• Erlang - will fail (inelegantly?) if shape parameter invalid.

Continuous fit distributions with no fit method at present:

• ErlangK - not sure how to fit.
• Poisson - requires data to be sorted times between events, can't enforce that.
• Hyperexponential - not sure how to fit.

Other distributions with no fit method:

• Bernoulli - categorical
• FixedDistribution - not applicable (single value)
• CombinationDistribution - combination
• GroupedContinuousEmpirical - natively fits to sample as it's an empirical distribution
• RawContinuousEmpirical - natively fits to sample as it's an empirical distribution
• DiscreteEmpirical - categorical
• TruncatedDistribution - truncation
• RawDiscreteEmpirical - categorical