The Gompertz Inverted Nadarajah-Haghighi (GoINH) Distribution Properties with Application to real data

Over the past years, many academics in mathematical statistics have introduced new continuous distributions to respond to real-world data growth, and this adaptability or flexibility has become essential to this development. In this study, a new distribution called Gompertz Inverted Nadarajah-Haghighi (GoINH) is proposed, according to the Gompertz family which is a new four-parameter probability distribution model. In addition, we will present a number of properties of the proposed distribution such as moment generating function, survival function, risk function, characteristic function, quantile function, pdf expansion, and ordered statistics which represent a few of the many mathematical and statistical features of the recently proposed model. The model parameters were also estimated using the maximum likelihood method. In the end, a practical application was carried out on real data, represented by failure times for 40 heavy-duty locomotive engines, and comparison with a number of new or known distributions to determine the efficiency of the distribution using a number of informatics criteria is using the R programming language.