Abstract
Based on the Nadarajah Haghighi distribution and the Topp Leone-G family in view of the T-X family, we introduce a new generator of continuous distributions with three extra parameters called the Nadarajah Haghighi Topp Leone-G family. Three sub-models of the new class are discussed. Main mathematical properties of the new family are investigated such as; quantile function, raw and incomplete moments, Bonferroni and Lorenz curves, moment and probability generating functions, stress-strength model, Shanon and Rényi entropies, order statistics and probability weighted moments. The model parameters of the new family is estimated by using the method of maximum likelihood and the observed information matrix is also obtained. We introduce two real applications to show the importance of the new family.
Highlights
In the last decade, the famous distributions such as Lomax, Pareto, Gumbel, Lindley,...etc are extensively used for fitting data in various sciences such as medicine, engineering, agriculture and economics
Based on the idea of T-X family pioneerd by Alzaatreh et al (2013), TL-G class and the Nadarajah Haghighi distribution, we introduce a new class of continuous distributions called the Nadarajah Haghighi Topp Leone-G (NHTL-G for short) family with cdf given by
We introduce two real applications to show the importance of the new family called the Nadarajah Haghighi Topp Leone-G family based on the Nadarajah Haghighi distribution, the T-X and TL-G classes
Summary
The famous distributions such as Lomax, Pareto, Gumbel, Lindley,...etc are extensively used for fitting data in various sciences such as medicine, engineering, agriculture and economics. In many applied areas such as environmental sciences, reliability studies and finance, there exist a great need to generalize these distributions to gain more acuracyand flexibility. Based on this reason, the statistican propose new methods for generating new generators of distributions to gain more desirable properties in the resulting distributions. Al-Shomrani et al. Based on the idea of T-X family pioneerd by Alzaatreh et al (2013), TL-G class and the Nadarajah Haghighi distribution, we introduce a new class of continuous distributions called the Nadarajah Haghighi Topp Leone-G (NHTL-G for short) family with cdf given by.
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