Asymptotic cumulants of the Bayes modal estimators of item parameters using marginal likelihood in item response theory are derived up to the fourth order with added higher-order asymptotic variances under possible model misspecification. Among them, only the first asymptotic cumulant and the...

We present a theoretical model that enables to predict population distribution according to fertility and survival rates for each age group. Using World Bank data, we estimated the relation between fertility rate of change and survival probabilities. Our findings show that fertility rate of...