We apply a recently developed computational approach‎ ‎test (CAT) to the one-way fixed effects ANOVA models of log-normal‎ ‎data with unequal variances‎. ‎The merits of the proposed test are‎ ‎numerically compared with the existing tests‎ - ‎the James second‎ ‎order test‎, ‎the Welch test and the Alexander-Govern test‎ - ‎with‎ ‎respect to their sizes and powers in different combinations of‎ ‎parameters and various sample sizes‎. ‎The simulation results‎ ‎demonstrate that the proposed method is‎ ‎satisfactory‎: ‎its type I error probability is very close to the nominal level‎. ‎We illustrate these approaches using a real example.

In this paper‎, ‎some recurrence relations are presented for the single and product moments of progressively Type-II right censored order statistics from a Pareto distribution‎. ‎These relations are obtained for a progressively censored sample from Pareto distribution with fixed and random removals‎, ‎where in the random case‎, ‎the number of units removed at each failure time follows a binomial distribution‎. ‎In addition‎, ‎Thomas-Wilson's Mixture Formula for Moments are obtained with with fixed and random removals‎. ‎Finally‎, ‎a numerical study is carried out to compare real and simulation results based on biases and MSEs of the expected termination time.