Precise large deviations for widely orthant dependent random variables with different distributions

Let [Formula: see text] be a sequence of random variables with different distributions [Formula: see text]. The partial sums are denoted by [Formula: see text], [Formula: see text]. This paper mainly investigates the precise large deviations of [Formula: see text], for the widely orthant dependent random variables [Formula: see text]. Under some mild conditions, the lower and upper bounds of the precise large deviations of the partial sums [Formula: see text], [Formula: see text], are presented.