covariance matrix $B_N$. Then in the case where $N_1$ eigenvalues of $\Sigma_N$ is $a$ and $N-N_1$ is $1$, the joint probability density function (j.p.d.f) for the eigenvalues of $B_N$ is given by $$\label{eq:jpdf1}
\mathcal{P}(y)=\frac{1}{Z_{M,N}}\prod_{i<j}(y_i-y_j)\prod_{j=1}^Ny_{j}^{M-N}\det\left[
y_k^{d^N_j-1}e^{-Ma_j^{-1}y_k}\right]_{1\leq j,k,\leq N},$$ where $Z_{M,N}$ is a normalization constant and $d^N_j$, $a_j$ are given by $$\begin{split}
d^N_j&=j,\quad a_j=1,\quad 1\leq j\leq N-N_1,\\
d^N_j&=j-N+N_1,\quad a_j=a,\quad N-N_1< j\leq N.
\end{split}$$ In this paper we will study the asymptotic limit of the Wishart distribution with $\frac{N}{M}\rightarrow c$ and $\frac{N_1}{N}\rightarrow\beta$ as $M$, $N\rightarrow\infty$ in such a way that $0<\beta,c<1$. In this case, the empirical distribution function (e.d.f) $F_N$ of the eigenvalues will converge weakly to a nonrandom p.d.f. $F$, which will be supported on either 1 or 2 intervals in $\mathbb{R}_+$. By applying the results of [@CS] to our case, we can extract properties of the measure $F$ from the solutions of an algebraic equation (See Section \[se:Stie\] for details) $$\label{eq:curve20}
\begin{split}
za\xi^3&+(A_2z+B_2)\xi^2+(z+B_1)\xi+1=0,\\
A_2&=(1+a),\quad B_2=a(1-c),\\
B_1&=1-c(1-\beta)+a(1-c\beta).
\end{split}$$ The results in [@CS] imply that the real zeros of the function $\frac{d z(\xi)}{d\xi}$ determines the boundary points of the support of $F$. Since the zeros of $\frac{d z(\xi)}{d\xi}$ coincide with the zeros of the following quartic polynomial, $$\label{eq:quartic1}
\begin{split}
a^2(1-c)\xi^4
&+2(a^2(1-c\beta)+a(1-c(1-\beta))\xi^3\\
&+(1-c(1-\beta)+a^2(1-c\beta)+4a)\xi^2 +2(1+a)\xi+1=0,
