The Inverted Nadarajah–Haghighi Power Series Distributions

In this study, a new class of distribution is introduced called the inverted Nadarajah–Haghighi power series. The new family is derived by compounding inverted Nadarajah–Haghighi and power series distributions. The new class contains some new probability distributions such as inverted Nadarajah–Haghighi logarithmic distribution, inverted Nadarajah–Haghighi geometric distribution, and inverted Nadarajah–Haghighi Poisson distribution. Some statistical properties of the new class are derived. The maximum likelihood estimation procedure is used to estimate the model parameters. Furthermore, a Monte Carlo Simulation is carried out to check the behavior of derived maximum likelihood estimators. The potentiality of the proposed family is assessed via two data sets from different fields. The best-fitted probability distribution is chosen using goodness-of-fit criteria. © 2023, The Author(s), under exclusive licence to Springer Nature India Private Limited.