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Abstract
In recent years, mixture distributions have been introduced which are very important in several areas, such as public health, engineering, economic, actuarial science, biomedical studies and industrial reliability. Compounding of statistical distributions, which arises when sampling from inhomogeneous populations (or mixed populations) with a different probability density function in each component. Size frequency distributions in animal populations with distinct age groups, the distribution of times to failure in a mixture of good and defective items, and the distribution of some diagnostic measure in a mixed population of patients, some of whom have a given disease and some of whom do not, are all examples of mixed distributions. In this research, a new three parameter lifetime distribution, called lomax poisson, with decreasing failure rate has been introduced. This distribution has been obtained by mixing lomax distribution and zero truncated poisson distribution. Closed form expressions for the density, cumulative distribution, survival and failure rate are provided. The rth raw moment of the new distribution and moment generating function are obtained. Estimation of the unknown parameters using different methods is considered. Based on numerical study, comparisons are made between the different estimators through their biases and mean squared errors. Additionally, a new three parameter lifetime distribution named the complementary burr III Poisson distribution is proposed. This distribution is obtained by mixing the distribution of the maximum of a random number of identically; independent burr III distributed random variables and zero truncated Poisson random variable