Multivariate lognormal and sinh-1-normal random vectors, members of the Johnson family, can be generated by direct transformation of multinormal random vectors. Formulae for specifying the parameters of the multinomial distribution in terms of the first and second order moments of the desired multivariate lognormal or sinh-1-normal distribution are given. These results facilitate the use of these distributions in Monte Carlo studies. In some previous studies employing these distributions, the effect of non-normality was confounded with that of unequal covariance structure.