Exponential distribution

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CDF

1 − e − λ x {\displaystyle 1-e^{-\lambda x}}

CF

λ λ − i t {\displaystyle {\frac {\lambda }{\lambda -it}}}

Entropy

1 − ln ⁡ λ {\displaystyle 1-\ln \lambda }

Excess kurtosis

6 {\displaystyle 6}

Fisher information

1 λ 2 {\displaystyle {\frac {1}{\lambda ^{2}}}}

Kullback–Leibler divergence

ln ⁡ λ 0 λ + λ λ 0 − 1 {\displaystyle \ln {\frac {\lambda _{0}}{\lambda }}+{\frac {\lambda }{\lambda _{0}}}-1}