A stochastic order for interval valued random mappings and applications

•Comparison of random intervals with respect to the distance to the origin in terms of a stochastic order.•Sufficient statistically testable conditions on the endpoints of the random intervals to confirm comparisons.•Applications in climatology and economy with interval valued data. This manuscript introduces a criterion to compare interval valued random mappings by means of a stochastic order for such random elements. The comparison criterion is based on the distance to the origin on both sides of the values that those random elements assume. The proposed stochastic order is studied, providing characterizations and properties. One of those characterizations is based on a new stochastic order for bivariate random vectors when it is applied to the endpoints of the random intervals. Some examples with applications of the criterion to weather and economic problems are developed.