Exponential-logarithmic distribution: Difference between revisions

Revision as of 03:54, 1 November 2009

Revision as of 03:56, 1 November 2009

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<TR>

<TH>Support</TH>

<TD><math>x\in(0,\infty)</math></TD></TR>

<TR>

<TH>Probability density function (pdf)</TH>

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<TR>

<TH>Mean</TH>

<TD><math>-\frac{\text{polylog}(2,1-p)}{\beta\ln p}</math></TD></TR>

<TR>

<TH>Median</TH>

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<TR>

<TH>Variance</TH>

<TD><math>-\frac{2 \text{polylog}(3,1-p)}{\beta^2\ln p}-\frac{ \text{polylog}^2(2,1-p)}{\beta^2\ln^2 p}</math></TD></TR>

<TR>

<TH>Skewness</TH>

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<TR>

<TH>Moment-generating function (mgf)</TH>

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

<TR>

<TH>Characteristic function</TH>