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A New Continuous Distribution and Two New Families of Distributions Based on the Exponential

Author

Listed:
  • Jasso, Guillermina

    (New York University)

  • Kotz, Samuel

    (George Washington University)

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, which we call 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 potential for broad application in diverse contexts across science and engineering, including the physical and social sciences as well as finance, information processing, and communication. 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

  • Jasso, Guillermina & Kotz, Samuel, 2007. "A New Continuous Distribution and Two New Families of Distributions Based on the Exponential," IZA Discussion Papers 2598, Institute of Labor Economics (IZA).
    • Handle: RePEc:iza:izadps:dp2598
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    Cited by:

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

    More about this item

    Keywords

    wage distribution; wage inequality; social inequality; wage function; social status; Gini coefficient; folded distributions; gamma distribution; Erlang distribution; continuous univariate distributions;
    All these keywords.

    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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