A new lifetime class with decreasing failure rateis introduced by compounding truncated Geometric distribution
and 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. A formal
equation for Fisher information matrix is derived in order to obtaining the asymptotic covariance matrix. This new
class of distributions generalizes several distributions which have been introduced and studied in the literature.