[ENH] Histogram distribution

skpro/distributions/histogram.py

@@ -0,0 +1,145 @@
+# copyright: skpro developers, BSD-3-Clause License (see LICENSE file)
+"""Histogram distribution."""
+
+__author__ = ["ShreeshaM07"]
+
+import numpy as np
+
+from skpro.distributions.base import BaseDistribution
+
+
+class Histogram(BaseDistribution):
+    """Histogram Probability Distribution.
+
+    The histogram probability distribution is parameterized
+    by the bins and bin densities.
+
+    Parameters
+    ----------
+    bins : float or array of float 1D
+        array has the bin boundaries with 1st element the first bin's
+        starting point and rest are the bin ending points of all bins
+    bin_mass: array of float 1D
+        Mass of the bins or Area of the bins.
+        Sum of all the bin_mass must be 1.
+    index : pd.Index, optional, default = RangeIndex
+    columns : pd.Index, optional, default = RangeIndex
+    """
+
+    def __init__(self, bins, bin_mass, index=None, columns=None):
+        self.bins = bins
+        self.bin_mass = bin_mass
+
+        super().__init__(index=index, columns=columns)
+
+    def _mean(self):
+        """Return expected value of the distribution.
+
+        Returns
+        -------
+        float, sum(bin_mass)/range(bins)
+            expected value of distribution (entry-wise)
+        """
+        bins = self.bins
+        # 1 is the cumulative sum of all bin_mass
+        return 1 / (max(bins) - min(bins))
+
+    def _var(self):
+        r"""Return element/entry-wise variance of the distribution.
+
+        Returns
+        -------
+        2D np.ndarray, same shape as ``self``
+            variance of the distribution (entry-wise)
+        """
+        bins = self.bins
+        bin_mass = self.bin_mass
+        bin_width = np.diff(bins)
+        mean = self._mean()
+        var = np.sum((bin_mass / bin_width - mean) * bin_width) / (
+            max(bins) - min(bins)
+        )
+        return var
+
+    def _pdf(self, x):
+        """Probability density function.
+
+        Parameters
+        ----------
+        x : 1D np.ndarray, same shape as ``self``
+            values to evaluate the pdf at
+
+        Returns
+        -------
+        1D np.ndarray, same shape as ``self``
+            pdf values at the given points
+        """
+        bin_mass = np.array(self.bin_mass.copy())
+        bins = self.bins
+        pdf = []
+        if isinstance(bins, list):
+            bin_width = np.diff(bins)
+            pdf_arr = bin_mass / bin_width
+            for X in x:
+                if len(np.where(X < bins)[0]) and len(np.where(X >= bins)[0]):
+                    pdf.append(pdf_arr[min(np.where(X < bins)[0]) - 1])
+                else:
+                    pdf.append(0)
+            pdf = np.array(pdf)
+            return pdf
+
+    def _cdf(self, x):
+        """Cumulative distribution function.
+
+        Parameters
+        ----------
+        x : 1D np.ndarray, same shape as ``self``
+            values to evaluate the cdf at
+
+        Returns
+        -------
+        1D np.ndarray, same shape as ``self``
+            cdf values at the given points
+        """
+        bins = self.bins
+        bin_mass = self.bin_mass
+        cdf = []
+        pdf = self._pdf(x)
+        if isinstance(bins, list):
+            for X in x:
+                # cum_bin_index is an array of all indices
+                # of the bins or bin edges that are less than X.
+                cum_bin_index = np.where(X >= bins)[0]
+                X_index_in_x = np.where(X == x)
+                if len(cum_bin_index) == len(bins):
+                    cdf.append(1)
+                elif len(cum_bin_index) > 1:
+                    cdf.append(
+                        np.cumsum(bin_mass)[-2]
+                        + pdf[X_index_in_x][0] * (X - bins[cum_bin_index[-1]])
+                    )
+                elif len(cum_bin_index) == 0:
+                    cdf.append(0)
+                elif len(cum_bin_index) == 1:
+                    cdf.append(pdf[X_index_in_x][0] * (X - bins[cum_bin_index[-1]]))
+            cdf = np.array(cdf)
+        return cdf
+
+
+# import pandas as pd
+
+# x = np.array([100, 1, 0.75, 1.8, 2.5, 3, 5, 6, 6.5, 0])
+# hist = Histogram(
+#     bins=[0.5, 2, 7],
+#     bin_mass=[0.3, 0.7],
+#     index=pd.Index(np.arange(3)),
+#     columns=pd.Index(np.arange(2)),
+# )
+# pdf = hist._pdf(x)
+# print(pdf)
+# cdf = hist._cdf(x)
+# print(cdf)
+# mean = hist._mean()
+# print(mean)
+# var = hist._var()
+# print(var)