Alternative Equation Formats

$$\begin{array}{rcl}{M}_{i,i^{\mathrm{\prime <!--\; \prime \; -->}}}& =\{& \text{number of times }{X}_{i,j}<X_{i^{\mathrm{\prime <!--\; \prime \; -->}},j^{\mathrm{\prime <!--\; \prime \; -->}}},j=1,\dots <!--\; \dots \; -->,n_{i.};j^{\mathrm{\prime <!--\; \prime \; -->}}=1,\dots <!--\; \dots \; -->,n_{i^{\mathrm{\prime <!--\; \prime \; -->}}.}\}\\ & +\frac{1}{2}\{& \text{number of times }{X}_{i,j}=X_{i^{\mathrm{\prime <!--\; \prime \; -->}},j^{\mathrm{\prime <!--\; \prime \; -->}}},j=1,\dots <!--\; \dots \; -->,n_{i.};j^{\mathrm{\prime <!--\; \prime \; -->}}=1,\dots <!--\; \dots \; -->,n_{i^{\mathrm{\prime <!--\; \prime \; -->}}.}\}\end{array}$$

$$\begin{array}{rcl}{M}_{i,i^{\mathrm{\prime <!--\; \prime \; -->}}}& =\{& \text{number of times }{X}_{i,j}<X_{i^{\mathrm{\prime <!--\; \prime \; -->}},j^{\mathrm{\prime <!--\; \prime \; -->}}},j=1,\dots <!--\; \dots \; -->,n_{i.};j^{\mathrm{\prime <!--\; \prime \; -->}}=1,\dots <!--\; \dots \; -->,n_{i^{\mathrm{\prime <!--\; \prime \; -->}}.}\}\\ & +\frac{1}{2}\{& \text{number of times }{X}_{i,j}=X_{i^{\mathrm{\prime <!--\; \prime \; -->}},j^{\mathrm{\prime <!--\; \prime \; -->}}},j=1,\dots <!--\; \dots \; -->,n_{i.};j^{\mathrm{\prime <!--\; \prime \; -->}}=1,\dots <!--\; \dots \; -->,n_{i^{\mathrm{\prime <!--\; \prime \; -->}}.}\}\end{array}$$

\begin{eqnarray*} M_{i,i^\prime } & = \hspace{.2in} \{ & \mbox{number of times } X_{i,j} < X_{i^\prime ,j^\prime }, \hspace{.1in} j=1,\ldots ,n_{i.}; \hspace{.08in} j^\prime =1,\ldots ,n_{i^\prime .} ~ \} \\ & + \hspace{0.05in} \frac{1}{2} \hspace{.1in} \{ & \mbox{number of times } X_{i,j} = X_{i^\prime ,j^\prime }, \hspace{.1in} j=1,\ldots ,n_{i.}; \hspace{.08in} j^\prime =1,\ldots ,n_{i^\prime .} ~ \} \end{eqnarray*}