some new features

.venv/lib/python3.12/site-packages/statsmodels/sandbox/distributions/try_pot.py

@@ -0,0 +1,66 @@
+"""
+Created on Wed May 04 06:09:18 2011
+
+@author: josef
+"""
+import numpy as np
+
+
+def mean_residual_life(x, frac=None, alpha=0.05):
+    '''empirical mean residual life or expected shortfall
+
+    Parameters
+    ----------
+    x : 1-dimensional array_like
+    frac : list[float], optional
+        All entries must be between 0 and 1
+    alpha : float, default 0.05
+        FIXME: not actually used.
+
+    TODO:
+        check formula for std of mean
+        does not include case for all observations
+        last observations std is zero
+        vectorize loop using cumsum
+        frac does not work yet
+    '''
+
+    axis = 0  # searchsorted is 1d only
+    x = np.asarray(x)
+    nobs = x.shape[axis]
+    xsorted = np.sort(x, axis=axis)
+    if frac is None:
+        xthreshold = xsorted
+    else:
+        xthreshold = xsorted[np.floor(nobs * frac).astype(int)]
+    # use searchsorted instead of simple index in case of ties
+    xlargerindex = np.searchsorted(xsorted, xthreshold, side='right')
+
+    # TODO:replace loop with cumsum ?
+    result = []
+    for i in range(len(xthreshold)-1):
+        k_ind = xlargerindex[i]
+        rmean = x[k_ind:].mean()
+        # this does not work for last observations, nans
+        rstd = x[k_ind:].std()
+        rmstd = rstd/np.sqrt(nobs-k_ind)  # std error of mean, check formula
+        result.append((k_ind, xthreshold[i], rmean, rmstd))
+
+    res = np.array(result)
+    crit = 1.96  # TODO: without loading stats, crit = -stats.t.ppf(0.05)
+    confint = res[:, 1:2] + crit * res[:, -1:] * np.array([[-1, 1]])
+    return np.column_stack((res, confint))
+
+
+expected_shortfall = mean_residual_life  # alias
+
+
+if __name__ == "__main__":
+    rvs = np.random.standard_t(5, size=10)
+    res = mean_residual_life(rvs)
+    print(res)
+    rmean = [rvs[i:].mean() for i in range(len(rvs))]
+    print(res[:, 2] - rmean[1:])
+
+    res_frac = mean_residual_life(rvs, frac=[0.5])
+    print(res_frac)