Probability distribution for size and mass of a nodule in the KR5 area for the development of a manganese nodule miner

In this paper, probability distribution for the size and mass of seafloor manganese nodules is investigated to improve the reliability of a pick-up device in a deep-sea manganese nodule miner. Because the size and mass of the manganese nodules are strongly correlated, statistical models for the size and mass cannot be estimated independently. In order to consider the correlation between the size and mass in a statistical model, the joint probability density function (PDF) is estimated by using copula. This method requires the estimation of the marginal distributions and copula for the two correlated environmental variables. However, this is significantly difficult when there is no prior knowledge of the two physical properties. The proposed method, which employs the Akaike information criterion to select the fittest marginal distributions and copula, provides a systematic procedure to determine a statistical model of correlated environmental variables without any prior knowledge of their distributions. To demonstrate the effectiveness of the proposed method, the joint PDF for the size and mass of manganese nodules is modeled by using the multivariate normal distribution and the proposed method. It was found that the proposed method provides more accurate and reliable estimation results for the two correlated environmental variables.