Exponential Probability Function

An Exponential Probability Function is an exponential function that is a probability density function from an exponential probability distribution family.

• AKA: Negative Exponential Probability Function.
• Context:
  • It can range from being a Univariate Exponential Probability Function to being a Multivariate Exponential Probability Function (such as a bivarate exponential distribution).
  • It can be expressed as [math]\displaystyle{ f(s) = (1/\lambda)e^{-s/\lambda} }[/math], where [math]\displaystyle{ \lambda }[/math] is a constant
• Example(s):
  • If λ=3000, [math]\displaystyle{ f }[/math](s) = (1/3000)e^-s/3000
  • a Logistic Sigmoid Curve Function.
  • a Gaussian Probability Function.
  • …
• Counter-Example(s):
  • a Poisson Probability Function.
• See: Lifetime Random Experiment, Generalized Linear Model.

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References

2006

• (Cox, 2006) ⇒ David R. Cox. (2006). “Principles of Statistical Inference." Cambridge University Press. ISBN:9780521685672

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