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A new continuous distribution and two new families of distributions based on the exponential

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  • Guillermina Jasso
  • Samuel Kotz

Abstract

Recent work on social status led to derivation of a new continuous distribution based on the exponential. The new variate, termed the ring(2)‐exponential, in turn leads to derivation of two closely related new families of continuous distributions, the mirror‐exponential and the ring‐exponential. Both the standard exponential and the ring(2)‐exponential are special cases of both the new families. In this paper, we first focus on the ring(2)‐exponential, describing its derivation and examining its properties, and next introduce the two new families, describing their derivation and initiating exploration of their properties. The mirror‐exponential arises naturally in the study of status; the ring‐exponential arises from the mathematical structure of the ring(2)‐exponential. Both have the potential for broad application in diverse contexts across science and engineering. Within sociobehavioral contexts, the new mirror‐exponential may have application to the problem of approximating the form and inequality of the wage distribution.

Suggested Citation

  • Guillermina Jasso & Samuel Kotz, 2007. "A new continuous distribution and two new families of distributions based on the exponential," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 61(3), pages 305-328, August.
    • Handle: RePEc:bla:stanee:v:61:y:2007:i:3:p:305-328
    DOI: 10.1111/j.1467-9574.2007.00358.x
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    Cited by:

    1. Guillermina Jasso & Samuel Kotz, 2008. "Two Types of Inequality," Sociological Methods & Research, , vol. 37(1), pages 31-74, August.
    2. Guillermina Jasso, 2009. "A New Model of Wage Determination and Wage Inequality," Rationality and Society, , vol. 21(1), pages 113-168, February.
    3. Jasso, Guillermina, 2009. "Linking Individuals and Societies," IZA Discussion Papers 4288, Institute of Labor Economics (IZA).
    4. Guillermina Jasso, 2021. "Linking Input Inequality and Outcome Inequality," Sociological Methods & Research, , vol. 50(3), pages 944-1005, August.

    More about this item

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • D6 - Microeconomics - - Welfare Economics
    • I3 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty

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