mostly API docs for ALT fitters and adding a few other docs

docs/How are the confidence intervals calculated.rst

@@ -0,0 +1,8 @@
+.. image:: images/logo.png
+
+-------------------------------------
+
+How are the confidence intervals calculated
+'''''''''''''''''''''''''''''''''''''''''''
+
+This is a placeholder for a theory document which will be written soon.

docs/How are the plotting positions calculated.rst

@@ -0,0 +1,8 @@
+.. image:: images/logo.png
+
+-------------------------------------
+
+How are the plotting positions calculated
+'''''''''''''''''''''''''''''''''''''''''
+
+This is a placeholder for a theory document which will be written soon.

docs/How does Least Squares Estimation work.rst

@@ -0,0 +1,8 @@
+.. image:: images/logo.png
+
+-------------------------------------
+
+How does Least Squares Estimation work
+''''''''''''''''''''''''''''''''''''''
+
+This is a placeholder for a theory document which will be written soon.

docs/How does Maximum Likelihood Estimation work.rst

@@ -0,0 +1,8 @@
+.. image:: images/logo.png
+
+-------------------------------------
+
+How does Maximum Likelihood Estimation work
+'''''''''''''''''''''''''''''''''''''''''''
+
+This is a placeholder for a theory document which will be written soon.

docs/Optimizers.rst

@@ -5,7 +5,8 @@
 Optimizers
 ''''''''''
 
-**What is an optimizer?**
+What is an optimizer?
+"""""""""""""""""""""
 
 An optimizer is an algorithm that uses two primary inputs; a target function and an initial guess. The optimizer's job is to figure out which input to the target function will minimise the output of the target function.
 
@@ -40,13 +41,15 @@ The optimizer that was used is always reported by each of the functions in `Fitt
                 BIC           19.3294
                  AD           3.72489 
 
-**Why do we need different optimizers?**
+Why do we need different optimizers?
+""""""""""""""""""""""""""""""""""""
 
 Each optimizer has various strengths and weaknesses because they work in different ways. Often they will arrive at the same result. Sometimes they will arrive at different results, either because of the very shallow gradient near the minimum, or the non-global minimum they have found. Sometimes they will fail entirely.
 
 There is no single best optimizer for fitting probability distributions so a few options are provided as described below.
 
-**Which optimizer should I pick?**
+Which optimizer should I pick?
+""""""""""""""""""""""""""""""
 
 You don't really need to worry about picking an optimizer as the default choice is usually sufficient. If you do want to select your optimizer, you have four to choose from. Most importantly, you should be aware of what the optimizer is doing (minimizing the negative log-likelihood equation by varying the parameters) and understand that optimizers aren't all the same which can cause different results. If you really need to know the best optimizer then select "best", otherwise you can just leave the default as None. 
 

docs/index.rst

@@ -26,7 +26,6 @@ Contents:
   :caption: Parametric Models
 
   Equations of supported distributions
-  What is censored data
   Creating and plotting distributions
   Fitting a specific distribution to data
   Fitting all available distributions to data
@@ -117,6 +116,16 @@ Contents:
   Distribution explorer
   Histogram
 
+.. toctree::
+  :maxdepth: 1
+  :caption: Reliability Theory
+
+  What is censored data
+  How are the plotting positions calculated
+  How does Least Squares Estimation work
+  How does Maximum Likelihood Estimation work
+  How are the confidence intervals calculated
+
 .. toctree::
   :maxdepth: 1
   :caption: Administration

reliability/Utils.py

@@ -3674,9 +3674,14 @@ def linear_regression(
         raise ValueError(err_str)
 
     if RRX_or_RRY == "RRY":
-        solution = (
-            np.linalg.inv(xx.T.dot(xx)).dot(xx.T).dot(yy)
-        )  # linear regression formula for RRY
+        try:
+            solution = (
+                np.linalg.inv(xx.T.dot(xx)).dot(xx.T).dot(yy)
+            )  # linear regression formula for RRY
+        except LinAlgError:
+            raise RuntimeError(
+                "An error has occurred when attempting to find the initial guess using least squares estimation.\nThis error is caused by a non-invertable matrix.\nThis can occur when there are only two very similar failure times like 10 and 10.000001.\nThere is no solution to this error, other than to use failure times that are more unique."
+            )
         if y_intercept is not None:
             m = solution[0]
             c = y_intercept
@@ -3687,9 +3692,14 @@ def linear_regression(
             m = solution[0]
             c = solution[1]
     else:  # RRX
-        solution = (
-            np.linalg.inv(yy.T.dot(yy)).dot(yy.T).dot(xx)
-        )  # linear regression formula for RRX
+        try:
+            solution = (
+                np.linalg.inv(yy.T.dot(yy)).dot(yy.T).dot(xx)
+            )  # linear regression formula for RRX
+        except LinAlgError:
+            raise RuntimeError(
+                "An error has occurred when attempting to find the initial guess using least squares estimation.\nThis error is caused by a non-invertable matrix.\nThis can occur when there are only two very similar failure times like 10 and 10.000001.\nThere is no solution to this error, other than to use failure times that are more unique."
+            )
         if x_intercept is not None:
             m_x = solution[0]
             m = 1 / m_x