A New Family of Distribution Based on the Bounded Marshall-Olkin Exponential Distribution: Properties and Applications

Abstract

A new family of distributions based on the bounded Marshall-Olkin exponential distribution. The new distribution known as the bounded Marshall-Olkin extended exponentially generated family of distributions. Various statistical properties, including the quantile function, characteristic function, moments and moment-generating function were derived for this new family. The distribution parameters were estimated using the maximum likelihood, ordinary least squares, and Cramér-von Mises procedures. In addition, the study explores three special distributions derived from the newly bounded Marshall-Olkin extended exponential-generated family. The hazard rates of these special distributions show their suitability for datasets exhibiting diverse non-monotonic failure rates. Monte Carlo simulations demonstrated the consistency of the estimators, with the maximum likelihood estimator showing superior performance compared to the other estimators. A location-scale regression model was conducted with data on long-term interest against direct foreign investment.  It was observed that long-term interest rates positively affect foreign direct investment with a 5% confidence level of significance for bounded Marshall-Olkin extended exponential Weibull and all the competing location-scale regression models.