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Abstract. This paper contains the results concerning the weak convergence of d-dimensional extreme order statistics in a Gaussian, equally correlated array. Three types of limit distributions are found and sufficient conditions for the existence of these distributions are given. Notation and definitions. Let {X (n) k: k ∈ {1, . . . , n}, n ∈ N} be a triangular array of d-dimensional random vectors whose mean values and variances satisfy d}) .We assume that (ii) the rows of the considered array are Gaussian equally correlated sequences.This means thatfor all i, j ∈ {1, . . . , d}, k, l ∈ {1, . . . , n}, k = l, n ∈ N. We denote the matrices of covariance coefficients byii ∈ (0, 1) for i ∈ {1, . . . , d}, n ∈ N .1991 Mathematics Subject Classification: Primary 60G70.

Nowadays the spread of precision forestry has led to the possibility of collecting data related to forest machines for an extended period and with enough precision to support decisions in the optimization of harvesting strategies in terms of technological and environmental efficiency. This study aims to evaluate the effective benefit of automatic data collection through the fleet management system (FMS) of two forest harvesters and two forwarders in pine forests in Poland. The study also aims to determine how the use of FMS can help forest companies to manage their fleet and take advantage of long-term monitoring. Focusing on performance indicators of fuel consumption and CO2 emissions, as well as on the engine parameters from the Can Bus data, the exploration of data was performed following a Big Data approach, from the creation of an aggregate dataset, pre-elaboration (data cleaning, exploration, selection, etc.) using GIS and R software. The investigation has considered the machine productivity, in the case of the harvesters, and the specific fuel consumption of each machine studied, as well as the time used by each of them during the different working cycle activities and the total amount of timber processed. The main results indicate an average emission of 2.1 kg of CO2 eq/m3 for the harvesters and 2.56 kg of CO2 eq/m3 for the forwarders, which equates in total to 0.24% of the carbon stored in one cubic meter of wood.