<p>The motivation for this paper comes from a dataset compiled by the US Insurance Services Office, which is dedicated to studying losses and their related Allocated Loss Adjustment Expenses (ALAE). This dataset features Type-I censoring on loss and associated variable ALAE, placing it in the category of Type-I concomitant censoring. The challenge addressed in this paper is selecting the appropriate model for this specific scenario. Five parameter bivariate Weibull and bivariate lognormal distributions are two bivariate distributions for studying positive lifetime bivariate data. These two distributions have striking similarities right from the surface plot of their joint density function to the nature of their reliability function. Along with that, the shape of their marginal distributions are also quite similar. This paper aims to discriminate between these two distributions under bivariate Type-I censoring based on induced order statistics. In this work, the difference between the maximized log-likelihood values of two models is employed as the basis for discriminating between the corresponding distribution functions. The asymptotic distribution of this discrimination statistic is derived and subsequently used to evaluate the probability of correct selection. To assess the performance of the proposed approach, Monte Carlo experiments are carried out. In addition, a modified version of the discrimination rule is proposed. The effect of model misspecification on correlation estimates is also investigated. Finally, an illustrative example based on a real data set is presented.</p>