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Abstract
Various recent probability distributions discussed modeling of such data by compounding the well-known lifetime distributions such as exponential, Weibull, generalized exponential, exponentiated Weibull{u2026}etc with some discrete distributions such as zero-truncated binomial, geometric, Poisson, logarithmic and the power series distributions in general. In this thesis, we compound the log-exponentiated Kumaraswamy power series family of distributions; this procedure follows similar way that was formerly carried out adamidis and loukas (1998). This new distribution is called log-exponentiated Kumaraswamy-power series (Log-EKPS) distributions. This family contains several new distributions. We discussed some properties of the Log-EKPS. The method of maximum likelihood is used for estimating the model parameters. An application to a real data set is analyzed to illustrate the flexibility of the new distributions. Also, we discuss a new compounding distribution called the complementary exponentiated Nadarajah-Haghighi power series (CENHPS) distribution; it is constructed based on a latent complementary risk problem. We discussed some properties of the new compounding. The estimation of the model parameters is performed by maximum likelihood method. Applications to real data sets are given to show the flexibility and potentiality of the proposed family of distributions