Computes the pdf, cdf, value at risk and expected shortfall for the complementary beta distribution due to Jones (2002) given by

*\begin{array}{ll}
&\displaystyle
f (x) = B (a, b)
≤ft\{ I_x^{-1} (a, b) \right\}^{1 - a}
≤ft\{ 1 - I_x^{-1} (a, b) \right\}^{1 - b},
\\
&\displaystyle
F (x) = I_x^{-1} (a, b),
\\
&\displaystyle
{\rm VaR}_p (X) = I_p (a, b),
\\
&\displaystyle
{\rm ES}_p (X) = \frac {1}{p} \int_0^p I_v (a, b) dv
\end{array}*

for *0 < x < 1*, *0 < p < 1*, *a > 0*, the first shape parameter, and *b > 0*, the second shape parameter.

1 2 3 4 | ```
dcompbeta(x, a=1, b=1, log=FALSE)
pcompbeta(x, a=1, b=1, log.p=FALSE, lower.tail=TRUE)
varcompbeta(p, a=1, b=1, log.p=FALSE, lower.tail=TRUE)
escompbeta(p, a=1, b=1)
``` |

`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 |

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

`b` |
the value of the second 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

1 2 3 4 5 | ```
x=runif(10,min=0,max=1)
dcompbeta(x)
pcompbeta(x)
varcompbeta(x)
escompbeta(x)
``` |

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