# skfolio.distribution.BaseUnivariateDist ### *class* skfolio.distribution.BaseUnivariateDist(random_state=None) Base Univariate Distribution Estimator. This abstract class serves as a foundation for univariate distribution models based on scipy. random_state *int, RandomState instance or None, default=None* : Seed or random state to ensure reproducibility. * **Attributes:** [`fitted_repr`](#skfolio.distribution.BaseUnivariateDist.fitted_repr) : String representation of the fitted univariate distribution. [`n_params`](#skfolio.distribution.BaseUnivariateDist.n_params) : Number of model parameters. ### Methods | [`aic`](#skfolio.distribution.BaseUnivariateDist.aic)(X) | Compute the Akaike Information Criterion (AIC) for the model given data X. | |-------------------------------------------------------------------------|----------------------------------------------------------------------------------------| | [`bic`](#skfolio.distribution.BaseUnivariateDist.bic)(X) | Compute the Bayesian Information Criterion (BIC) for the model given data X. | | [`cdf`](#skfolio.distribution.BaseUnivariateDist.cdf)(X) | Compute the cumulative distribution function (CDF) for the given data. | | [`fit`](#skfolio.distribution.BaseUnivariateDist.fit)(X[, y]) | Fit the univariate distribution model. | | [`get_metadata_routing`](#skfolio.distribution.BaseUnivariateDist.get_metadata_routing)() | Get metadata routing of this object. | | [`get_params`](#skfolio.distribution.BaseUnivariateDist.get_params)([deep]) | Get parameters for this estimator. | | [`plot_pdf`](#skfolio.distribution.BaseUnivariateDist.plot_pdf)([X, title]) | Plot the probability density function (PDF). | | [`ppf`](#skfolio.distribution.BaseUnivariateDist.ppf)(X) | Compute the percent point function (inverse of the CDF) for the given | | [`qq_plot`](#skfolio.distribution.BaseUnivariateDist.qq_plot)(X[, title]) | Plot the empirical quantiles of the sample X versus the quantiles of the fitted model. | | [`sample`](#skfolio.distribution.BaseUnivariateDist.sample)([n_samples]) | Generate random samples from the fitted distribution. | | [`score`](#skfolio.distribution.BaseUnivariateDist.score)(X[, y]) | Compute the total log-likelihood under the model. | | [`score_samples`](#skfolio.distribution.BaseUnivariateDist.score_samples)(X) | Compute the log-likelihood of each sample (log-pdf) under the model. | | [`set_params`](#skfolio.distribution.BaseUnivariateDist.set_params)(\*\*params) | Set the parameters of this estimator. | #### aic(X) Compute the Akaike Information Criterion (AIC) for the model given data X. The AIC is defined as: $$ \mathrm{AIC} = -2 \, \log L \;+\; 2 k, $$ where - $\log L$ is the total log-likelihood - $k$ is the number of parameters in the model A lower AIC value indicates a better trade-off between model fit and complexity. * **Parameters:** **X** *array-like of shape (n_observations, n_features)* : The input data on which to compute the AIC. * **Returns:** **aic** *float* : The AIC of the fitted model on the given data. ### Notes In practice, both AIC and BIC measure the trade-off between model fit and complexity, but BIC tends to prefer simpler models for large $n$ because of the $\ln(n)$ term. ### References * **[1]** “A new look at the statistical model identification”, Akaike (1974). #### bic(X) Compute the Bayesian Information Criterion (BIC) for the model given data X. The BIC is defined as: $$ \mathrm{BIC} = -2 \, \log L \;+\; k \,\ln(n), $$ where - $\log L$ is the (maximized) total log-likelihood - $k$ is the number of parameters in the model - $n$ is the number of observations A lower BIC value suggests a better fit while imposing a stronger penalty for model complexity than the AIC. * **Parameters:** **X** *array-like of shape (n_observations, n_features)* : The input data on which to compute the BIC. * **Returns:** **bic** *float* : The BIC of the fitted model on the given data. ### Notes In practice, both AIC and BIC measure the trade-off between model fit and complexity, but BIC tends to prefer simpler models for large $n$ because of the $\ln(n)$ term. ### References * **[1]** “Estimating the dimension of a model”, Schwarz, G. (1978). #### cdf(X) Compute the cumulative distribution function (CDF) for the given data. * **Parameters:** **X** *array-like of shape (n_observations, 1)* : Data points at which to evaluate the CDF. * **Returns:** **cdf** *ndarray of shape (n_observations, 1)* : The CDF evaluated at each data point. #### *abstractmethod* fit(X, y=None) Fit the univariate distribution model. * **Parameters:** **X** *array-like of shape (n_observations, 1)* : The input data. X must contain a single column. **y** *None* : Ignored. Provided for compatibility with scikit-learn’s API. * **Returns:** **self** *BaseUnivariateDist* : Returns the instance itself. #### *property* fitted_repr String representation of the fitted univariate distribution. #### get_metadata_routing() Get metadata routing of this object. Please check [User Guide](https://skfolio.org/user_guide/metadata_routing.html.md#metadata-routing) on how the routing mechanism works. * **Returns:** **routing** *MetadataRequest* : A `MetadataRequest` encapsulating routing information. #### get_params(deep=True) Get parameters for this estimator. * **Parameters:** **deep** *bool, default=True* : If True, will return the parameters for this estimator and contained subobjects that are estimators. * **Returns:** **params** *dict* : Parameter names mapped to their values. #### *property* n_params Number of model parameters. #### plot_pdf(X=None, title=None) Plot the probability density function (PDF). * **Parameters:** **X** *array-like of shape (n_samples, 1), optional* : If provided, it is used to plot the empirical data KDE for comparison versus the model PDF. **title** *str, optional* : The title for the plot. If not provided, a default title based on the fitted model’s representation is used. * **Returns:** **fig** *go.Figure* : A Plotly figure object containing the PDF plot. #### ppf(X) Compute the percent point function (inverse of the CDF) for the given : probabilities. * **Parameters:** **X** *array-like of shape (n_observations, 1)* : Probabilities for which to compute the corresponding quantiles. * **Returns:** **ppf** *ndarray of shape (n_observations, 1)* : The quantiles corresponding to the given probabilities. #### qq_plot(X, title=None) Plot the empirical quantiles of the sample X versus the quantiles of the fitted model. * **Parameters:** **X** *array-like of shape (n_samples, 1), optional* : Used to plot the empirical quantiles for comparison versus the model quantiles. **title** *str, optional* : The title for the plot. If not provided, a default title based on the fitted model’s representation is used. * **Returns:** **fig** *go.Figure* : A Plotly figure object containing the PDF plot. #### sample(n_samples=1) Generate random samples from the fitted distribution. Currently, this is implemented only for gaussian and tophat kernels. * **Parameters:** **n_samples** *int, default=1* : Number of samples to generate. * **Returns:** **X** *array-like of shape (n_samples, 1)* : List of samples. #### score(X, y=None) Compute the total log-likelihood under the model. * **Parameters:** **X** *array-like of shape (n_observations, n_features)* : An array of data points for which the total log-likelihood is computed. **y** *None* : Ignored. Provided for compatibility with scikit-learn’s API. * **Returns:** **logprob** *float* : The total log-likelihood (sum of log-pdf values). #### score_samples(X) Compute the log-likelihood of each sample (log-pdf) under the model. * **Parameters:** **X** *array-like of shape (n_observations, 1)* : An array of points at which to evaluate the log-probability density. The data should be a single feature column. * **Returns:** **density** *ndarray of shape (n_observations,)* : Log-likelihood values for each observation in X. #### set_params(\*\*params) Set the parameters of this estimator. The method works on simple estimators as well as on nested objects (such as `Pipeline`). The latter have parameters of the form `__` so that it’s possible to update each component of a nested object. * **Parameters:** **\*\*params** *dict* : Estimator parameters. * **Returns:** **self** *estimator instance* : Estimator instance.