In this paper, a new lifetime class with decreasing failure rate is introduced by compounding truncated binomial distribution with any proper continuous lifetime distribution. The properties of the proposed class are discussed, including a formal proof of its probability density function, distribution function and explicit algebraic formulae for its reliability and failure rate functions. A simple EM-type algorithm for iteratively computing maximum likelihood estimates is presented. The Fisher information matrix is derived in order to obtain the asymptotic covariance matrix. This new class of distributions generalizes several distributions which have been introduced and studied in the literature.
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