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Exponential and hypoexponential distributions: Some characterizations

Mathematics, ISSN: 2227-7390, Vol: 8, Issue: 12, Page: 1-10
2020
  • 9
    Citations
  • 718
    Usage
  • 12
    Captures
  • 2
    Mentions
  • 64
    Social Media
Metric Options:   Counts1 Year3 Year

Metrics Details

  • Citations
    9
    • Citation Indexes
      9
  • Usage
    718
  • Captures
    12
  • Mentions
    2
    • Blog Mentions
      1
      • Blog
        1
    • References
      1
      • 1
  • Social Media
    64
    • Shares, Likes & Comments
      64
      • Facebook
        64

Article Description

The (general) hypoexponential distribution is the distribution of a sum of independent exponential random variables. We consider the particular case when the involved exponential variables have distinct rate parameters. We prove that the following converse result is true. If for some n ≥ 2, X, X, …, X are independent copies of a random variable X with unknown distribution F and a specific linear combination of X ’s has hypoexponential distribution, then F is exponential. Thus, we obtain new characterizations of the exponential distribution. As corollaries of the main results, we extend some previous characterizations established recently by Arnold and Villaseñor (2013) for a particular convolution of two random variables.

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