Merge pull request #7 from rickecon/chaps

Merging

Author: rickecon

docs/book/_toc.yml

@@ -36,7 +36,7 @@ parts:
   - caption: Appendix
     chapters:
     - file: appendix/glossary
-    - file: appendix/intro
+    - file: appendix/appendix
   - caption: References
     chapters:
     - file: CompMethods_references

docs/book/appendix/appendix.md

@@ -0,0 +1,23 @@
+(Chap_Appendix)=
+# Appendix
+
+Put Appendix intro here.
+
+(SecAppendixTruncNormal)=
+## Truncated normal distribution
+
+The truncated normal distribution with parameters $\mu$ and $\sigma$ and lower-bound cutoff $c_{lb}$ and upper-bound cutoff $c_{ub}$ is simply the normal distribution of values of the random variable $x$ defined only on the interval $x\in[c_{lb}, c_{ub}]$ rather than on the full real line. And the probability distribution function values are upweighted by the probability (less than one) under the normal distribution on the interval $[c_{lb}, c_{ub}]$.
+```{math}
+    :label: EqAppendix_TruncNorm
+    \text{truncated normal:}\quad &f(x|\mu,\sigma,c_{lb},c_{ub}) = \frac{\phi(x|\mu,\sigma)}{\Phi(c_{ub}|\mu,\sigma) - \Phi(c_{ub}|\mu,\sigma)} \\
+    &\text{where}\quad \phi(x|\mu,\sigma) \equiv \frac{1}{\sqrt{2\pi\sigma^2}}e^{-\frac{x - \mu}{2\sigma^2}} \\
+    &\text{and}\quad \Phi(x|\mu,\sigma) \equiv \int_{-\infty}^x\phi(x|\mu,\sigma) dx
+```
+
+The function $\phi(x|\mu,\sigma)$ is the probability distribution function of the normal distribution with mean $\mu$ and variance $\sigma^2$. And the function $\Phi(x|\mu,\sigma)$ is the cummulative distribution function of the normal distribution with mean $\mu$ and variance $\sigma^2$.
+
+
+(SecAppendixFootnotes)=
+## Footnotes
+
+The footnotes from this appendix.

docs/book/appendix/intro.md

@@ -98,4 +98,6 @@ A good introduction to structural estimation is to compare it to other types of
 (SecStructEstIntroFootnotes)=
 ## Footnotes
 
+The footnotes from this chapter.
+
 [^MACSScourses]: I taught a course, entitled Structural Estimation, to graduate students, with a few advanced undergradutates, in the Masters in Computational Social Science program at the University of Chicago four times from 2017 to 2020. The content of each course is in the following GitHub repositories, with syllabi, lecture slides, Jupyter notebooks, tests, and problem sets: [Winter 2017](https://github.com/rickecon/StructEst_W17), [Winter 2018](https://github.com/rickecon/StructEst_W18), [Winter 2019](https://github.com/rickecon/StructEst_W19), and [Winter 2020](https://github.com/rickecon/StructEst_W20).