توزیع نمایی

Key facts

Parameters

0,"}}'> λ > 0 , {\displaystyle \lambda >0,} rate, or inverse scale

Support

x ∈ [ 0 , ∞ ) {\displaystyle x\in [0,\infty )}

Pdf

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

Cdf

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

Quantile

− ln ⁡ ( 1 − p ) λ {\displaystyle -{\frac {\ln(1-p)}{\lambda }}}

Mean

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

Median

ln ⁡ 2 λ {\displaystyle {\frac {\ln 2}{\lambda }}}

Mode

0 {\displaystyle 0}

Variance

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

Skewness

2 {\displaystyle 2}

Excess kurtosis

6 {\displaystyle 6}

Entropy

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

Mgf

λ λ − t , for t < λ {\displaystyle {\frac {\lambda }{\lambda -t}},{\text{ for }}t<\lambda }

Cf

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

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}

via Wikipedia infobox