Computes pdf of the arc tan model.

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`x` |
scalar or vector of values to compute the pdf. |

`alpha` |
the value of |

`spec` |
a character string specifying the parent distribution (for example, "lnorm" if the parent distribution corresponds to the lognormal). |

`arg` |
list of arguments/parameters of the parent distribution. |

`log` |
logical; if |

The pdf of arc tan model with parameter *α* has a general form of:

*
f(x) = \frac{1}{\arctan(α)} \frac{α g(x)}{1 + (α (1-G(x)))^{2}}
*

for *a≤q x≤q b* where *a* and *b* follow the support of *g(x)*. *\arctan* denote the inverse function of tangent. *g(x)* and *G(x)* are the pdf and cdf of parent distribution, respectively. Note also that *α>0*.

An object of the same length as `x`

, giving the pdf values computed at `x`

.

Shaiful Anuar Abu Bakar

S.A. Abu Bakar, S. Nadarajah, Z.A. ABSL Kamarul Adzhar, I. Mohamed. gendist: An R package for generated probability distribution models, submitted.

Gomez-Deniz, E., & Calderin-Ojeda, E. Modelling insurance data with the pareto arctan distribution. ASTIN Bulletin, 1-22.

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