Empirical Application of Generalized Rayleigh Distribution for Mineral Resource Estimation of Seabed Polymetallic Nodules

An efficient empirical statistical method is developed to improve the process of mineral resource estimation of seabed polymetallic nodules and is applied to analyze the abundance of seabed polymetallic nodules in the Clarion Clipperton Zone (CCZ). The newly proposed method is based on three hypotheses as the foundation for a model of “idealized nodules”, which was validated by analyzing nodule samples collected from the seabed within the Tonga Offshore Mining Limited (TOML) exploration contract. Once validated, the “idealized nodule” model was used to deduce a set of empirical formulae for predicting the nodule resources, in terms of percentage coverage and abundance. The formulae were then applied to analyzing a total of 188 sets of nodule samples collected across the TOML areas, comprising box-core samples and towed camera images as well as other detailed box-core sample measurements from the literature. Numerical results for nodule abundance and coverage predictions were compared with field measurements, and unbiased agreement has been reached. The new method has the potential to achieve more accurate mineral resource estimation with reduced sample numbers and sizes. They may also have application in improving the efficiency of design and configuration of mining equipment.

Empirical Application of Generalized Rayleigh Distribution for Mineral Resource Estimation of Seabed Polymetallic Nodules

An effective empirical statistical method is developed to improve the process of mineral resource estimation of seabed polymetallic nodules and is applied to analyse the abundance of seabed polymetallic nodules in the Clarion Clipperton Zone (CCZ). The newly proposed method is based on three hypotheses as the foundation for a model of “Idealized Nodules”, which was validated by analysing nodule samples collected from the seabed within the Tonga Offshore Mining Limited (TOML) exploration contract. Once validated, the “Idealized Nodule” model was used to deduce a set of empirical formulae for predicting the nodule resources, in terms of Percentage Coverage and Abundance. The formulae were then applied to analysing a total of 188 sets of nodule samples collected across the TOML areas, comprising box-core samples and towed camera images collected by one of the authors and detailed in [4]. The analysis also relies upon detailed box-core sample measurements from other areas reported by [7]. Numerical results for resource prediction were compared with field measurements, and reasonable agreement has been achieved. The new method has the potential to achieve more accurate mineral resource estimation with reduced sample numbers and sizes. They may also have application in improving the efficiency of design and configuration of mining equipment.

Risk Analysis by a Probabilistic Model of the Measurement Process

The aim of the article is presentation of the testing methodology and results of examination the probabilistic model of the measurement process. The case study concerns the determination of the risk of an incorrect decision in the assessment of the compliance of products by measurement. Measurand is characterized by the generalized Rayleigh distribution. The model of the measurement process was tested in parallel mode by six risk metrics. An undesirable effect in the reconstruction building block of the model was detected, consisting in the distortion of probability distribution at the edges of the measuring range. The paper gives guidelines on how to use the model, to obtain the analytical risk assessment consistent with the results of the Monte Carlo method. The study can be useful in product quality control, test design, and fault diagnosis.

STATISTICAL INFERENCE FOR GEOMETRIC PROCESS WITH THE GENERALIZED RAYLEIGH DISTRIBUTION

In the present paper, statistical inference problem is considered for the geometric process (GP) by assuming the distribution of the first arrival time is generalized Rayleigh with the parameters $\alpha$ and $\lambda$. We use the maximum likelihood method for obtaining the ratio parameter of the GP and distributional parameters of the generalized Rayleigh distribution. By a series of Monte-Carlo simulations evaluated through the different samples of sizes small, moderate and large, we also compare the estimation performances of the maximum likelihood estimators with the other estimators available in the literature such as modified moment, modified L-moment, and modified least squares. Furthermore, we present two real-life dataset analyzes to show the modeling behavior of GP with generalized Rayleigh distribution.