Let X λ 1 , X λ 2 , . . . , X λn be independent Weibull random variables with X λ i ∼ W (α, λi) where λi > 0, for i = 1, . . . , n. Let X λ n:n denote the lifetime of the parallel system formed from X λ 1 , X λ 2 , . . . , X λn . We investigate the effect of the changes in the scale parameters (λ1, . . . , λn) on the magnitude of X λ n:n according to reverse hazard rate and likelihood ratio orderings.

In this work, we discuss stochastic comparisons between the largest order statistics from multiple-outlier models when the numbers of independent and identically distributed random variables are different. That is, if X n:n (p, q) is the largest order statistic among

Excess of deaths is a technique used in epidemiology to assess the deaths caused by an unexpected event. For the present COVID–19 pandemic, we discuss the performance of some linear and nonlinear time series forecasting techniques widely used for modeling the actual pandemic and provide estimates for this metric from January 2020 to April 2021. We apply the results obtained to evaluate the evolution of the present pandemic in Brazil and Spain, which allows in particular to compare how well (or bad) these countries have managed the pandemic. For Brazil, our calculations refute the claim made by some officials that the present pandemic is “a little flu”. Some studies suggest that the virus could be lying dormant across the world before been detected for the first time. In that regard, our results show that there is no evidence of deaths by the virus in 2019.

No abstract

Let X λ 1 , X λ 2 , . . . , X λn be independent nonnegative random variables with X λ i ∼ F (λ i t), i = 1, . . . , n, where λ i > 0, i = 1, . . . , n and F is an absolutely continuous distribution. It is shown that, under some conditions, one largest order statistic X λ n:n is smaller than another one X θ n:n according to likelihood ratio ordering. Furthermore, we apply these results when F is a generalized gamma distribution which includes Weibull, gamma and exponential random variables as special cases.Keywords: likelihood ratio order; reverse hazard rate order; majorization; order statistics Mathematics Subject Classification (2010) 62G30 ; 60E15 ; 60K10 rate of the (maximum) minimum in bivariate distributions. Metrika 63, 223-241. Hu, T. (1995). Monotone coupling and stochastic ordering of order statistics. Syst. Sci. Math. Sci. 8, 209-214. Joo, S. and Mi, J. (2010). Some properties of hazard rate functions of systems with two components.