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Composition of distribution functions is considered one of the methods that generate new distributions. In this paper, a new distribution is obtained by composing a log-logistic distribution with a Weibull distribution. The new distribution has decreasing and unimodal shapes of the hazard rate function which make it suitable to fit several real data. Some properties of the new distribution are investigated. Based on progressive type-II censoring, the maximum likelihood, moments and probability weighted moments estimation methods for the involved parameters are studied and compared through a simulation study. The asymptotic confidence intervals for the parameters are also obtained based on asymptotic variance-covariance matrix. Finally, real data are used to compare the new distribution with four lifetime distributions based on five comparison criteria. The comparison shows that the new distribution is better to fit the data than the other four distributions.

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