Exponential Distribution - Related Distributions

Related Distributions

• Exponential distribution is closed under scaling by a positive factor. If then

• If and then

• If then

• The Benktander Weibull distribution reduces to a truncated exponential distribution

• If then (Benktander Weibull distribution)

• The exponential distribution is a limit of a scaled beta distribution:

• If then (Erlang distribution)

• If then (Generalized extreme value distribution)

• If then (gamma distribution)

• If and then (Laplace distribution)

• If and then

• If then

• If then (logistic distribution)

• If and then (logistic distribution)

• If then (Pareto distribution)

• If then

• Exponential distribution is a special case of type 3 Pearson distribution

• If then (power law)

• If then (Rayleigh distribution)

• If then (Weibull distribution)

• If then (Weibull distribution)

• If (Uniform distribution (continuous)) then

• If (Poisson distribution) where then (geometric distribution)

• If and then (K-distribution)

• The Hoyt distribution can be obtained from Exponential distribution and Arcsine distribution

• If and then

• If and then

• If, then : see skew-logistic distribution.

• Y ∼ Gumbel(μ, β), i.e. Y has a Gumbel distribution, if Y = μ − βlog(Xλ) and X ∼ Exponential(λ).

• X ∼ χ₂2, i.e. X has a chi-squared distribution with 2 degrees of freedom, if .

• Let X ∼ Exponential(λ_X) and Y ∼ Exponential(λ_Y) be independent. Then has probability density function . This can be used to obtain a confidence interval for .

Other related distributions:

• Hyper-exponential distribution – the distribution whose density is a weighted sum of exponential densities.
• Hypoexponential distribution – the distribution of a general sum of exponential random variables.
• exGaussian distribution – the sum of an exponential distribution and a normal distribution.