Small corrections.

man/diststudent.Rd

@@ -2,7 +2,7 @@
 % Please edit documentation in R/diststudent.R
 \name{diststudent}
 \alias{diststudent}
-\title{Distance/Divergence between Centered Multivariate $t$ Distributions}
+\title{Distance/Divergence between Centered Multivariate \eqn{t} Distributions}
 \usage{
 diststudent(nu1, Sigma1, nu2, Sigma2,
                    dist = c("renyi", "bhattacharyya", "hellinger"),
@@ -45,7 +45,7 @@ Let \eqn{\delta_1 = \frac{\nu_1 + p}{2} \beta}, \eqn{\delta_2 = \frac{\nu_2 + p}
 and \eqn{\lambda_1, \dots, \lambda_p} the eigenvalues of the square matrix \eqn{\Sigma_1 \Sigma_2^{-1}}
 sorted in increasing order: \deqn{\lambda_1 < \dots < \lambda_{p-1} < \lambda_p}
 The Renyi divergence between \eqn{X_1} and \eqn{X_2} is:
-\deqn{D_R^\beta(\mathbf{X}_1||\mathbf{X}_1) = \frac{1}{\beta - 1} \bigg[ \beta \ln\left(\frac{\Gamma\left(\frac{\nu_1+p}{2}\right) \Gamma\left(\frac{\nu_2}{2}\right) \nu_2^{\frac{p}{2}}}{\Gamma\left(\frac{\nu_2+p}{2}\right) \Gamma\left(\frac{\nu_1}{2}\right) \nu_1^{\frac{p}{2}}}\right) + \ln\left(\frac{\Gamma\left(\frac{\nu_2+p}{2}\right)}{\Gamma\left(\frac{\nu_2}{2}\right)}\right) + \ln\left(\frac{\Gamma\left(\delta_1 + \delta_2 - \frac{p}{2}\right)}{\Gamma(\delta_1 + \delta_2)}\right) - \frac{\beta}{2} \sum_{i=1}^p{\ln\lambda_i} + \ln F_D^{(p)}{\bigg( \delta_1, \frac{1}{2}, \dots, \frac{1}{2}; \delta_1+\delta_2; 1-\frac{\nu_2}{\nu_1 \lambda_1}, \dots, 1-\frac{\nu_2}{\nu_1 \lambda_p} \bigg)} \bigg]}
+\deqn{D_R^\beta(\mathbf{X}_1||\mathbf{X}_1) = \frac{1}{\beta - 1} \bigg[ \beta \ln\left(\frac{\Gamma\left(\frac{\nu_1+p}{2}\right) \Gamma\left(\frac{\nu_2}{2}\right) \nu_2^{\frac{p}{2}}}{\Gamma\left(\frac{\nu_2+p}{2}\right) \Gamma\left(\frac{\nu_1}{2}\right) \nu_1^{\frac{p}{2}}}\right) + \ln\left(\frac{\Gamma\left(\frac{\nu_2+p}{2}\right)}{\Gamma\left(\frac{\nu_2}{2}\right)}\right) + \ln\left(\frac{\Gamma\left(\delta_1 + \delta_2 - \frac{p}{2}\right)}{\Gamma(\delta_1 + \delta_2)}\right) - \frac{\beta}{2} \sum_{i=1}^p{\ln\lambda_i} + \ln F_D^{(p)}{\bigg( \delta_1, \underbrace{\frac{1}{2}, \dots, \frac{1}{2}}_p; \delta_1+\delta_2; 1-\frac{\nu_2}{\nu_1 \lambda_1}, \dots, 1-\frac{\nu_2}{\nu_1 \lambda_p} \bigg)} \bigg]}
 
 where \eqn{F_D^{(p)}} is the Lauricella \eqn{D}-hypergeometric function defined for \eqn{p} variables:
 \deqn{ \displaystyle{ F_D^{(p)}\left(a; b_1, ..., b_p; g; x_1, ..., x_p\right) = \sum\limits_{m_1 \geq 0} ... \sum\limits_{m_p \geq 0}{ \frac{ (a)_{m_1+...+m_p}(b_1)_{m_1} ... (b_p)_{m_p} }{ (g)_{m_1+...+m_p} } \frac{x_1^{m_1}}{m_1!} ... \frac{x_p^{m_p}}{m_p!} } } }
@@ -55,7 +55,7 @@ The Bhattacharyya distance is given by:
 \deqn{D_B(\mathbf{X}_1||\mathbf{X}_2) = \frac{1}{2} D_R^{1/2}(\mathbf{X}_1||\mathbf{X}_2)}
 
 And the Hellinger distance is given by:
-\deqn{D_B(\mathbf{X}_1||\mathbf{X}_2) = 1 - \exp{-\frac{1}{2} D_R^{1/2}(\mathbf{X}_1||\mathbf{X}_2)}}
+\deqn{D_H(\mathbf{X}_1||\mathbf{X}_2) = 1 - \exp{\left(-\frac{1}{2} D_R^{1/2}(\mathbf{X}_1||\mathbf{X}_2)\right)}}
 }
 \examples{
 \donttest{