Statistical Properties and Different Methods of Estimation for Type I Half Logistic Inverted Kumaraswamy Distribution

In this paper, we introduce and study a new three-parameter lifetime distribution constructed from the so-called type I half-logistic-G family and the inverted Kumaraswamy distribution, naturally called the type I half-logistic inverted Kumaraswamy distribution. The main feature of this new distribution is to add a new tuning parameter to the inverted Kumaraswamy (according to the type I half-logistic structure), with the aim to increase the flexibility of the related inverted Kumaraswamy model and thus offering more precise diagnostics in data analyses. The new distribution is discussed in detail, exhibiting various mathematical and statistical properties, with related graphics and numerical results. An exhaustive simulation was conducted to investigate the estimation of the model parameters via several well-established methods, including the method of maximum likelihood estimation, methods of least squares and weighted least squares estimation, and method of Cramer-von Mises minimum distance estimation, showing their numerical efficiency. Finally, by considering the method of maximum likelihood estimation, we apply the new model to fit two practical data sets. In this regards, it is proved to be better than recent models, also derived to the inverted Kumaraswamy distribution.