Abstract
In this article, we introduce a new general family of distributions derived to the truncated inverted Kumaraswamy distribution (on the unit interval), called the truncated inverted Kumaraswamy generated family. Among its qualities, it is characterized with tractable functions, has the ability to enhance the flexibility of a given distribution, and demonstrates nice statistical properties, including competitive fits for various kinds of data. A particular focus is given on a special member of the family defined with the exponential distribution as baseline, offering a new three-parameter lifetime distribution. This new distribution has the advantage of having a hazard rate function allowing monotonically increasing, decreasing, and upside-down bathtub shapes. In full generality, important properties of the new family are determined, with an emphasis on the entropy (Rényi and Shannon entropy). The estimation of the model parameters is established by the maximum likelihood method. A numerical simulation study illustrates the nice performance of the obtained estimates. Two practical data sets are then analyzed. We thus prove the potential of the new model in terms of fitting, with favorable results in comparison to other modern parametric models of the literature.
Highlights
The inverted Kumaraswamy distribution was introduced by [1], with the motivation to offer a new flexible lifetime distribution with tractable distributional properties
Having in mind the aim to explore new statistical horizons, we aim to benefit from the qualities of the inverted Kumaraswamy distribution to create a new general family of distributions
We introduce a special member of the family defined with the exponential distribution as baseline, forming a new three-parameter lifetime distribution called truncated inverted
Summary
The inverted Kumaraswamy distribution was introduced by [1], with the motivation to offer a new flexible lifetime distribution with tractable distributional properties. We propose to truncate the inverted Kumaraswamy distribution on the unit interval and to compose it with a general cdf of a continuous distribution. Such a truncation technique has been employed with success to define new general families from well-established distributions on the semi-interval (0, +∞). Defining the truncated inverted Kumaraswamy generated (TIK-G) family of distribution. We introduce a special member of the family defined with the exponential distribution as baseline, forming a new three-parameter lifetime distribution called truncated inverted.
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