The Gompertz Nadarajah-Haghighi (GoNH) Distribution Properties with Application to Real Data

Abstract

In this study, we propose a continuous statistical distribution consisting of four parameters based on
the Gompertz family called the Gompertz Nadarajah-Haghighi (GoNH) distribution. Adding parameters to the
basic distribution provides the distribution with flexibility and efficiency in analysing real-world data. The model
that was recently suggested has many mathematical and statistical properties. Explicit formulas for its moments,
moment-generating function, survival function, risk function, characteristic function, quantile function, expansion
of pdf, and ordered statistics are only a few of the many mathematical and statistical features of the recently
proposed model. The maximum likelihood estimates (MLE) method was used to estimate the model’s parameters.
We conducted various simulation experiments to thoroughly evaluate the small sample of MLEs. The research
examined the estimators’ bias and mean square error, yielding positive outcomes. The study’s results demonstrated
that the GoNH distribution fit better than other distributions in two real-world data applications.