fix some typos and make some improvements

slides/sections/1.md

@@ -1,5 +1,5 @@
 # Goal
- 
+
 
 ## Goal
 
@@ -87,7 +87,7 @@ utilized in the approximation of the former.
 - Kolmogorov - Smirnov:
   - compatibility between expected and observed CDF
 
-. . . 
+. . .
 
 - Trapani test:
-  - compatibiity between expected and observed mean
+  - compatibility between expected and observed momenta

slides/sections/2.md

@@ -12,7 +12,7 @@ Because of its fat tail:
 
 . . .
 
-No closed form for parameters $\thus$ Numerical estimations
+No closed form for parameters $\thus$ numerical estimations
 
 
 ## Landau median
@@ -35,7 +35,7 @@ $$
 
 ## Landau mode
 
-- Maxmimum $\quad \Longrightarrow \quad \partial_x L(\mu) = 0$
+- Maximum $\quad \Longrightarrow \quad \partial_x L(\mu) = 0$
 
 . . .
 

slides/sections/3.md

@@ -20,7 +20,7 @@ More generally:
 $$
   z = \frac{x - \mu}{\sigma}
   \thus
-  M(x) = \frac{1}{\sqrt{2 \pi} \sigma} \exp
+  M_{\mu \sigma}(x) = \frac{1}{\sqrt{2 \pi} \sigma} \exp
          \left[ - \frac{1}{2} \left(
            \frac{x - \mu}{\sigma}
            + e^{-\frac{x - \mu}{\sigma}} \right) \right]
@@ -60,7 +60,7 @@ $$
 
 ## Moyal QDF
 
-The quantile (CDF\textsuperscript{-1}) is found solving:
+The quantile (CDF\textsuperscript{-1}) is found solving for $x$:
 $$
   y = 1 - \text{erf} \left( \frac{e^{- \frac{x}{2}}}{\sqrt{2}} \right)
 $$

slides/sections/4.md

@@ -40,7 +40,7 @@ Most probable value
 HSM
 
 - Iteratively identify the smallest interval containing half points
-- once the sample is reduced to less than three points, take average
+- Once the sample is reduced to less than three points, take average
 
 
 ## Sample FWHM
@@ -60,7 +60,7 @@ $$
   G \left( \frac{x-x_i}{\varepsilon} \right)
 $$
 
-The parameter $\varepsilon$ controls the strenght of the smoothing
+The parameter $\varepsilon$ controls the strength of the smoothing
 
 
 ## Sample FWHM
@@ -77,8 +77,8 @@ $$
 
 with:
 
-- $S_N$ is the sample stdev
+- $S_N$ is the sample standard deviation
-- $d$ number of dimensions ($d = 1$)
+- $d$ is number of dimensions ($d = 1$)
 
 . . .
 

slides/sections/5.md

@@ -33,7 +33,7 @@ $$
 $$
 
 $$
-  \implies \sigma_M \approx 1.1191486
+  \implies \sigma_M \approx 1.1191486...
 $$
 
 
@@ -60,7 +60,7 @@ This leads to more different medians:
 \end{align*}
 
 
-## Results compatibility
+## Compatibility test
 
 Comparing results:
 
@@ -70,7 +70,7 @@ $$
 $$
 
 - $x\ex$ and $x\ob$ are the expected and observed values
-- $\sigma_e$ and $\sigma_o$ are their absolute errors
+- $\sigma\ex$ and $\sigma\ob$ are their absolute errors
 
 . . .
 

slides/sections/6.md

@@ -15,7 +15,7 @@ $$
 gsl_ran_Landau(gsl_rng)
 
 
-## Compatiblity results:
+## Compatibility results:
 
 Median:
 
@@ -89,10 +89,10 @@ $$
 
 reverse sampling
 
-- sampling $y$ uniformly in [0, 1] $\quad \longrightarrow \quad x = Q_M(y)$ 
+- sampling $y$ uniformly in [0, 1] $\quad \longrightarrow \quad x = Q_M(y)$
 
 
-## Compatiblity results:
+## Compatibility results:
 
 Median: