Discrete Inverted Nadarajah-Haghighi Distribution: Properties and Classical Estimation with Application to Complete and Censored data

Abstract

In this article, we have developed the discrete version of the continuous inverted Nadarajah-Haghighi distribution and called it a discrete inverted Nadarajah-Haghighi distribution. The present model is well enough to model not only the over-dispersed and positively skewed data but it can also model upside-down bathtub-shaped, decreasing failure rate, and randomly right-censored data. Here, we have developed some important statistical properties for the proposed model such as quantile, median, moments, skewness, kurtosis, index of dispersion, entropy, expected inactivity time function, stress-strength reliability, and order statistics. We have estimated the model parameters through the method of maximum likelihood under complete and censored data. An algorithm to generate randomly right-censored data from the proposed model is also presented. The extensive simulation studies are presented to test the behavior of the estimators with complete and censored data. Finally, two complete and two censored data are used to illustrate the utility of the proposed model.