Research Article Open Access

A New Family: Σh Distributions

Rania Mustafa Shalabi1 and Yasser Mohamed Amer2
  • 1 The Higher Institute of Managerial Science, Egypt
  • 2 Cairo Higher Institutes in Mokattam, Egypt
Journal of Mathematics and Statistics
Volume 17 No. 1, 2021, 1-12


Submitted On: 27 September 2020 Published On: 7 January 2021

How to Cite: Shalabi, R. M. & Amer, Y. M. (2021). A New Family: Σh Distributions. Journal of Mathematics and Statistics, 17(1), 1-12.


In this study, a new method is proposed for generating families of the sum of the hazard functions for two distributions named the Σh distributions. This new family will help in the application of a wider range of life time data. Many new distributions, which are members of the family, are presented with emphasis on the Σh Exponential-Lomax distribution. Details and various statistical properties have been introduced. The maximum likelihood estimation for parameters of the Σh Exponential-Lomax distribution has also been discussed alongside Monte Carlo simulation study to assess the accuracy and the performance of the estimation procedure. Finally, the Σh Exponential-Lomax distribution has been fitted to a real data set to provide variability of its applicability.

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  • Hazard Functions
  • Lomax Distribution
  • Exponential Distribution
  • Maximum Likelihood
  • Monte Carlo