The Inverse Nakagami-m Distribution: A Novel Approach in Reliability

In the paper, the inverse Nakagami-m (NK) distribution is proposed. This distribution is the reciprocal of the NK-model that plays an important role in the general area of the communications engineering and reliability system. The proposed model is useful to describe devices that are subjected to high stress, providing high failure rate after a short repair time. An account of mathematical properties is presented such as the rth moment, mean, variance, rth central moment, survival properties, and Shannon's entropy. The maximum-likelihood estimators are explored under complete and censored data, but a bias correction was applied to the order O(n-2) for obtaining nearly unbiased performance. An efficient closed-form maximum a posteriori (MAP) estimator was also proposed. A simulation study compares the performance of the estimators with a clear advantage for the closed-form MAP one. Finally, we illustrate the new distribution fitting on three real datasets.