Exponential-logarithmic distribution: Difference between revisions

Revision as of 21:53, 1 May 2013

Revision as of 21:54, 1 May 2013

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| type = continuous

| pdf_image = [[File:Pdf EL.png|300px|Probability density function]]

| cdf_image =

| notation =

| parameters = <math>p\in (0,1)</math></SPANbr><BR><SPAN> <math>\beta >0</math>

| support = <math>x\in[0,\infty)</math>

| pdf = <math>\frac{1}{-\ln p} \times \frac{\beta(1-p) e^{-\beta x}}{1-(1-p) e^{-\beta x}}</math>

x}}{1-(1-p) e^{-\beta x}}</math>

| cdf = <math>1-\frac{\ln(1-(1-p) e^{-\beta x})}{\ln p}</math>

| mean = <math>-\frac{\text{polylog}(2,1-p)}{\beta\ln p}</math>

Line 14 ⟶ 13:

| mode = 0

| variance = <math>-\frac{2 \text{polylog}(3,1-p)}{\beta^2\ln p}</math><br> <math>-\frac{ \text{polylog}^2(2,1-p)}{\beta^2\ln^2 p}</math>

| skewness =

| kurtosis =

| entropy =

| mgf = <math>-\frac{\beta(1-p)}{\ln p (\beta-t)} \text{hypergeom}_{2,1} </math><br> <math>([1,\frac{\beta-t}{\beta}],[\frac{2\beta-t}{\beta}],1-p)</math>

| cf =

| pgf =

| fisher =

}}

In [[probability theory]] and [[statistics]], the '''exponential-logarithmic (EL) distribution''' is a family of lifetime [[probability distribution|distributions]] with