corrected some pages

Several small corrections were done to several proofs and definitions.

Author: JoramSoch

D/anova2.md

@@ -83,4 +83,4 @@ $$ \label{eq:anova2-cons}
 \end{split}
 $$
 
-where the weights are $w_{ij} = n_{ij}/n$ and the total sample size is $n = \sum_{i=1}^{a} \sum_{j=1}^{b} n_{ij}$.
+where the weights are $w_{ij} = n_{ij}/n$ and the total [sample size](/D/samp-size) is $n = \sum_{i=1}^{a} \sum_{j=1}^{b} n_{ij}$.

D/hyp-simp.md

@@ -29,6 +29,6 @@ username: "JoramSoch"
 
 **Definition:** Let $H$ be a [statistical hypothesis](/D/hyp). Then,
 
-* $H$ is called a simple hypothesis, if it completely specifies the population distribution; in this case, the [sampling distribution](/D/dist-samp) of the [test statistic](/D/tstat) is a function of sample size alone.
+* $H$ is called a simple hypothesis, if it completely specifies the population distribution; in this case, the [sampling distribution](/D/dist-samp) of the [test statistic](/D/tstat) is a function of [sample size](/D/samp-size) alone.
 
 * $H$ is called a composite hypothesis, if it does not completely specify the population distribution; for example, the hypothesis may only specify one parameter of the distribution and leave others unspecified.

P/anova2-ols.md

@@ -58,7 +58,7 @@ $$ \label{eq:mean-samp}
 \end{split}
 $$
 
-with the sample size numbers
+with the [sample size](/D/samp-size) numbers
 
 $$ \label{eq:samp-size}
 \begin{split}

P/ci-wilks.md

@@ -74,7 +74,7 @@ $$ \label{eq:llr}
 \log \Lambda(\phi) = \log p(y|\phi,\hat{\lambda}) - \log p(y|\hat{\phi},\hat{\lambda}) \; .
 $$
 
-[Wilks' theorem](/P/llr-wilks) states that, when comparing two statistical models with parameter spaces $\Theta_1$ and $\Theta_0 \subset \Theta_1$, as the sample size approaches infinity, the quantity calculated as $-2$ times the log-ratio of maximum likelihoods follows a [chi-squared distribution](/D/chi2), if the null hypothesis is true:
+[Wilks' theorem](/P/llr-wilks) states that, when comparing two statistical models with parameter spaces $\Theta_1$ and $\Theta_0 \subset \Theta_1$, as the [sample size](/D/samp-size) approaches infinity, the quantity calculated as $-2$ times the log-ratio of maximum likelihoods follows a [chi-squared distribution](/D/chi2), if the null hypothesis is true:
 
 $$ \label{eq:wilks}
 H_0: \theta \in \Theta_0 \quad \Rightarrow \quad -2 \log \frac{\operatorname*{max}_{\theta \in \Theta_0} p(y|\theta)}{\operatorname*{max}_{\theta \in \Theta_1} p(y|\theta)} \sim \chi^2_{\Delta k}  \quad \text{as} \quad n \rightarrow \infty

P/lognorm-prodind.md

@@ -33,7 +33,7 @@ $$ \label{eq:X-lognorm}
 X_i \sim \ln \mathcal{N}(\mu_i, \sigma_i^2), \; i = 1, \ldots, n \; .
 $$
 
-Then, the product of these random variables also follows a [log-normal distribution](/D/lognorm):
+Then, the product of these random variables also follows a [log-normal distribution](/D/lognorm)
 
 $$ \label{eq:Z-lognorm}
 Z = \prod_{i=1}^n X_i \sim \mathcal{N}(\mu, \sigma^2)
@@ -76,7 +76,7 @@ This means that the logarithm of the product of independent [log-normal](/D/logn
 $$ \label{eq:ln-Z-norm}
      \ln Z
 =    \sum_{i=1}^n Y_i
-\sim \mathcal{N}\left( \sum_{i=1}^n \mu_i, \sum_{i=1}^n \sigma_i^2 \right) \; .
+\sim \mathcal{N}\left( \sum_{i=1}^n \mu_i, \, \sum_{i=1}^n \sigma_i^2 \right) \; .
 $$
 
 If a random variable [follows a normal distribution, then its exponential follows a log-normal distribution with the same parameters]:
@@ -92,7 +92,7 @@ Thus, from \eqref{eq:ln-Z-norm}, we have
 $$ \label{eq:Z-lognorm-qed}
      Z
 =    \exp(\ln Z) 
-\sim \ln \mathcal{N}\left( \sum_{i=1}^n \mu_i, \sum_{i=1}^n \sigma_i^2 \right)
+\sim \ln \mathcal{N}\left( \sum_{i=1}^n \mu_i, \, \sum_{i=1}^n \sigma_i^2 \right)
 $$
 
 which is equivalent to \eqref{eq:Z-lognorm} and \eqref{eq:Z-lognorm-para}.