Add .igammac() term entry for PyTorch Tensor Operations (Issue #7793)

content/pytorch/concepts/tensor-operations/terms/igammac/igammac.md

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+---
+Title: '.igammac()'
+Description: 'Computes the regularized upper incomplete gamma function.'
+Subjects:
+  - 'Data Science'
+  - 'Machine Learning'
+Tags:
+  - 'AI'
+  - 'Deep Learning'
+  - 'Functions'
+  - 'Machine Learning'
+  - 'PyTorch'
+CatalogContent:
+  - 'intro-to-py-torch-and-neural-networks'
+  - 'paths/computer-science'
+---
+
+The **`torch.igammac()`** function in PyTorch computes the upper regularized incomplete gamma function. This function is commonly used in probabilistic modeling, survival analysis, and statistical machine learning applications. `torch.igammac()` is an alias for `torch.special.gammaincc()`, meaning both functions compute the same values and can be used interchangeably.
+
+## Syntax
+
+```pseudo
+torch.igammac(input, other, \*, out=None)
+```
+
+This is equivalent to:
+
+```pseudo
+torch.special.gammaincc(input, other, \*, out=None)
+```
+
+**Parameters:**
+
+- `input` (Tensor): The first non-negative input tensor representing the shape parameter (${a}$).
+- `other` (Tensor): The second non-negative input tensor representing the integration limit (${x}$).
+- `out` (Tensor, optional): The output tensor.
+
+**Return value:**
+
+Returns a tensor containing the upper regularized incomplete gamma function values for each corresponding pair of elements in `input` and `other`.
+
+> **Note:** Supports broadcasting to a common shape and requires float inputs. The backward pass with respect to `input` is not currently supported.
+
+## Example 1: Basic Element-Wise Computation
+
+In this example, `torch.igammac()` computes the upper regularized incomplete gamma function for corresponding elements of two 1D tensors:
+
+```py
+import torch
+
+a = torch.tensor([4.0])
+x = torch.tensor([3.0, 4.0, 5.0])
+
+result = torch.igammac(a, x)
+print("Upper incomplete gamma:", result)
+
+# Verify complementary relationship with igamma
+lower = torch.igamma(a, x)
+print("Sum of igamma and igammac:", lower + result)
+```
+
+This code produces the following output:
+
+```shell
+Upper incomplete gamma: tensor([0.6472, 0.4335, 0.2650])
+Sum of igamma and igammac: tensor([1., 1., 1.])
+```
+
+## Example 2: Survival Probabilities
+
+In this example, `torch.igammac()` calculates the survival probability (complement of CDF) for a gamma distribution at a given time point:
+
+```py
+import torch
+
+shape = torch.tensor([2.0, 3.0, 4.0])
+time = torch.tensor([1.5])
+
+survival_prob = torch.igammac(shape, time)
+cdf = torch.igamma(shape, time)
+
+print("Shape parameters:", shape)
+print("Time point:", time)
+print("Survival probabilities:", survival_prob)
+print("\nCDF values:", cdf)
+print("CDF + Survival:", cdf + survival_prob)
+```
+
+The output of this code is:
+
+```shell
+Shape parameters: tensor([2., 3., 4.])
+Time point: tensor([1.5])
+Survival probabilities: tensor([0.4422, 0.7127, 0.8221])
+
+CDF values: tensor([0.5578, 0.2873, 0.1779])
+CDF + Survival: tensor([1., 1., 1.])
+```