Computes the pdf, cdf, value at risk and expected shortfall for the exponential extension distribution due to Nadarajah and Haghighi (2011) given by

*\begin{array}{ll}
&\displaystyle
f (x) = a λ (1 + λ x)^{a - 1} \exp ≤ft[ 1 - (1 + λ x)^a \right],
\\
&\displaystyle
F (x) = 1 - \exp ≤ft[ 1 - (1 + λ x)^a \right],
\\
&\displaystyle
{\rm VaR}_p (X) = \frac {≤ft[ 1 - \log (1 - p) \right]^{1 / a} - 1}{λ},
\\
&\displaystyle
{\rm ES}_p (X) = -\frac {1}{λ} + \frac {1}{λ p} \int_0^p ≤ft[ 1 - \log (1 - v) \right]^{1 / a} dv
\end{array}*

for *x > 0*, *0 < p < 1*, *a > 0*, the shape parameter and *λ > 0*, the scale parameter.

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`x` |
scaler or vector of values at which the pdf or cdf needs to be computed |

`p` |
scaler or vector of values at which the value at risk or expected shortfall needs to be computed |

`lambda` |
the value of the scale parameter, must be positive, the default is 1 |

`a` |
the value of the shape parameter, must be positive, the default is 1 |

`log` |
if TRUE then log(pdf) are returned |

`log.p` |
if TRUE then log(cdf) are returned and quantiles are computed for exp(p) |

`lower.tail` |
if FALSE then 1-cdf are returned and quantiles are computed for 1-p |

An object of the same length as `x`

, giving the pdf or cdf values computed at `x`

or an object of the same length as `p`

, giving the values at risk or expected shortfall computed at `p`

.

Saralees Nadarajah

S. Nadarajah, S. Chan and E. Afuecheta, An R Package for value at risk and expected shortfall, submitted

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