Complementary Power Series Exponentiated Nadarajah-Haghighi Distribution

ABSTRACT

  A new class of distributions, called complementary power series exponentiated Nadarajah-Haghighi distribution was developed in this study by compounding the exponentiated Nadarajah-Haghighi distribution with zero truncated power series distributions. The new class of distributions were developed using the concepts of latent complementary risk scenario, in which the lifetime associated with a particular risk is not observable; rather we observe only the maximum lifetime value among all risks. The statistical properties such as quantile, moments, moment generating function, stochastic ordering property and order statistics for the new class of distributions were derived. In order to estimate the parameters of the new class of distributions, the maximum likelihood method was employed to develop estimators for the parameters. Special sub-distributions namely, complementary Poisson exponentiated Nadarajah-Haghighi, complementary geometric Nadarajah-Haghighi, complementary binomial Nadarajah-Haghighi and complementary logarithmic Nadarajah-Haghighi distributions were developed from the new class of distributions. A study of the failure rate of the special sub distributions revealed that they exhibit different kinds of non-monotonic failure rates including bathtub and upside-down bathtub. Monte Carlo simulations were performed to examine the behavior of the estimators and the results showed that the estimators were able to estimate the parameters well. The applications of the specials distributions were illustrated using two lifetime datasets and the results revealed that the special sub-distributions perform better than the exponentiated Nadarajah-Haghighi distribution.