GOLLG | R Documentation |

Computes the pdf, cdf, hdf, quantile and random numbers of the beta extended distribution due to Cordeiro et al. (2017) specified by the pdf

*f=\frac{αβ\,g\,G^{αβ-1}[1-G^α]^{β-1}}{[G^{αβ}+[1-G^α]^β]^2}*

for *G* any valid continuous cdf , *\bar{G}=1-G*, *g* the corresponding pdf, *α > 0*, the first shape parameter, and *β > 0*, the second shape parameter.

pgollg(x, alpha = 1, beta = 1, G = pnorm, ...) dgollg(x, alpha = 1, beta = 1, G = pnorm, ...) qgollg(q, alpha = 1, beta = 1, G = pnorm, ...) rgollg(n, alpha = 1, beta = 1, G = pnorm, ...) hgollg(x, alpha = 1, beta = 1, G = pnorm, ...)

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

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

`beta` |
the value of the second shape parameter, must be positive, the default is 1. |

`G` |
A baseline continuous cdf. |

`...` |
The baseline cdf parameters. |

`q` |
scaler or vector of probabilities at which the quantile needs to be computed. |

`n` |
number of random numbers to be generated. |

`pgollg`

gives the distribution function,
`dgollg`

gives the density,
`qgollg`

gives the quantile function,
`hgollg`

gives the hazard function and
`rgollg`

generates random variables from the Generalized Odd log-logistic family of
distributions (GOLL-G) for baseline cdf G.

Cordeiro, G.M., Alizadeh, M., Ozel, G., Hosseini, B., Ortega, E.M.M., Altun, E. (2017). The generalized odd log-logistic family of distributions : properties, regression models and applications. Journal of Statistical Computation and Simulation ,87(5),908-932.

x <- seq(0, 1, length.out = 21) pgollg(x) pgollg(x, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2) dgollg(x, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2) curve(dgollg, -3, 3) qgollg(x, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2) n <- 10 rgollg(n, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2) hgollg(x, alpha = 2, beta = 2, G = pbeta, shape1 = 1, shape2 = 2) curve(hgollg, -3, 3)

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