Abstract
We proposed a new family of lifetime distributions, namely, complementary exponentiated exponential geometric distribution. This new family arises on a latent competing risk scenario, where the lifetime associated with a particular risk is not observable but only the maximum lifetime value among all risks. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulas for its survival and hazard functions, moments,rth moment of theith order statistic, mean residual lifetime, and modal value. Inference is implemented via a straightforwardly maximum likelihood procedure. The practical importance of the new distribution was demonstrated in three applications where our distribution outperforms several former lifetime distributions, such as the exponential, the exponential-geometric, the Weibull, the modified Weibull, and the generalized exponential-Poisson distribution.
Highlights
Several new classes of models have been introduced in recent years grounded in the simple exponential distribution
We proposed a new family of lifetime distributions, namely, complementary exponentiated exponential geometric distribution
We can cite [1], which proposed a variation of the exponential distribution, the exponential geometric (EG) distribution, with decreasing hazard function, [2], which introduced the exponentiated exponential distribution as a generalization of the usual exponential distribution, which can accommodate data with increasing and decreasing hazard functions, [3], which proposed a generalized exponential distribution, which can accommodate data with increasing and decreasing hazard functions, [4], which proposed the exponentiated type distributions extending the Frechet, gamma, Gumbel, and Weibull distributions, [5], which proposed another modification of the exponential distribution with decreasing hazard function
Summary
Several new classes of models have been introduced in recent years grounded in the simple exponential distribution. The new distribution genesis is stated on a complementary risk problem base [9] in presence of latent risks, in the sense that there is no information about which factor was responsible for the component failure and only the maximum lifetime value among all risks is observed. This family have one shape and two scale parameters accommodating increasing, decreasing, and bathtub failure rates.
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