  In this paper ideas of different types of convergence of a sequence of random
variables in probability, namely, statistical convergence of order $\alpha$ in
probability, strong $p$-Ces$\grave{\mbox{a}}$ro summability of order $\alpha$
in probability, lacunary statistical convergence or $S_{\theta}$-convergence of
order $\alpha$ in probability, ${N_{\theta}}$-convergence of order $\alpha$ in
probability have been introduced and their certain basic properties have been
studied.
