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On some Bivariate Semi Parametric Families of Distributions with a Singular Component


The main idea of this paper is to present families of bivariate distributions that depend in their formation on adding a shape parameter to the powers of the hazard and reversed hazard functions in different manners, which would provide additional flexibility in applications. Different baseline distributions were used namely, exponential, inverse exponential, uniform, inverse uniform, inverse Rayleigh, Gompertz and Pareto. Many of the mathematical properties of these families are discussed in detail. Moreover, it is observed that the new bivariate distributions also can make appropriate modeling of three real data sets.

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  • Kundu, D. and Gupta, R.D. (2010). A class of Bivariate Models with Proportional Reversed Hazard Marginals. Sankhya, Ser B, 72, 236-253.

    MathSciNet  Article  Google Scholar 

  • Marshall, A.W. and Olkin, I. (1967). A multivariate exponential distribution. Journal of the American Statistical Association, 62, 30- 44.

    MathSciNet  Article  Google Scholar 

  • Marshall, A.W and Olkin, I. (2007). Life Distributions –Structure of Nonparametric, Semiparametri and Parametric Families, Springer, New York,

  • Meintanis, S. G. (2007). Test of fit for Marshall-Olkin distributions with applications. Journal of Statistical Planning and inference, 137, 3954–3963.

    MathSciNet  Article  Google Scholar 

  • Shoaee S (2020) On a New Class of Bivariate Survival Distributions Based on the Model of Dependent Lives and its Generalization, Applications and Applied Mathematics An International Journal 15(2):801 – 829.

    MathSciNet  MATH  Google Scholar 

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The author is profoundly grateful to the anonymous referees and editor for their valuable suggestions and comments which improved the earlier draft of the article.


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Correspondence to Hiba Zeyada Muhammed.

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Muhammed, H.Z. On some Bivariate Semi Parametric Families of Distributions with a Singular Component. Sankhya A (2022).

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  • Exponential distribution
  • Inverse exponential distribution
  • Uniform distribution, inverse uniform distribution
  • Inverse Rayleigh distribution
  • Gompertz Distribution and Pareto distribution