Let T=( $T_1$,…, $T_{k}$;k$geq$2) be a minimal sufficient and complete statistic for a k-parameter exponential model. Consider a partition of T into ( $T_1$, $T_2$), where $T_1$=( $T_1$,…, $T_{r}$ and $T_2$=( $T_{r+1}$,…, $T_{k}$1$leq$r$leq$k-1/). This article represents a way to obtain higher moments such as skewness and kurtosis for the distribution T and the conditional distribution of $T_1$, given $T_2$= $t_2$. These results are illustrated by some examples.s.les.s.