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In this paper, we introduce a new family of distributions which extends several new halfdistributions. Also, the family can be viewed as a general weighted family of distributions. Some general mathematical properties of the family are obtained, involving the quantile function, (conditional) moments, moment generating function, entropies, order statistics, record values and a bivariate extension of the family. Different estimation procedures for the family parameters are discussed. Somedoi:10.2298/fil2001257b fatcat:uubg3vjsmvg57baqpg7ulvtv2a