Pareto mix {extremefit} | R Documentation |

Density, distribution function, quantile function and random generation for the Pareto mixture distribution with *a* equal to the shape of the first Pareto Distribution, *b* equal to the shape of the second Pareto Distribution and *c* is the mixture proportion. The locations and the scales parameters are equals to *0* and *1*.

pparetomix(q, a = 1, b = 2, c = 0.75) dparetomix(x, a = 1, b = 2, c = 0.75) qparetomix(p, a = 1, b = 2, c = 0.75, precision = 10^(-10), initvalue = 0.5, Nmax = 1000) rparetomix(n, a = 1, b = 2, c = 0.75, precision = 10^(-10))

`q` |
a vector of quantiles. |

`a` |
the shape parameter of the first Pareto Distribution. |

`b` |
the shape parameter of the second Pareto Distribution. |

`c` |
the value of the mixture proportion. |

`x` |
a vector of quantiles. |

`p` |
a vector of probabilities. |

`precision` |
the precision of the Newton method. |

`initvalue` |
the initial value of the Newton method. |

`Nmax` |
the maximum of iteration done for the Newton method. |

`n` |
the number of observations. If length(n) > 1, the length is taken to be the number required. |

If the *a*, *b* and *c* are not specified, they respectively take the default values *1*, *2* and *0.75*.

The cumulative Pareto mixture distribution is

*
F(x) = c (1- x ^ {-a}) + ( 1 - c ) (1 - x ^ {-b}), x ≥ 1, a >0, b > 0, 0 ≤ c ≤ 1
*

where *a* and *b* are the shapes of the distribution and *c* is the mixture proportion.

dparetomix gives the density, pparetomix gives the distribution function, qparetomix gives the quantile function, and rparetomix generates random deviates.

The length of the result is determined by n for rparetomix, and is the maximum of the lengths of the numerical arguments for the other functions.

The numerical arguments other than n are recycled to the length of the result. Only the first elements of the logical arguments are used.

par(mfrow = c(3,1)) plot(function(x) dparetomix(x), 0, 5,ylab="density", main = " Pareto mixture density ") mtext("dparetomix(x)", adj = 0) plot(function(x) pparetomix(x), 0, 5,ylab="distribution function", main = " Pareto mixture Cumulative ") mtext("pparetomix(x)", adj = 0) plot(function(x) qparetomix(x), 0, 1,ylim=c(0,5),ylab="quantiles", main = " Pareto mixture Quantile ") mtext("qparetomix(x)", adj = 0) #generate a sample of the Pareto mix distribution of size n n <- 100 x <- rparetomix(n)

[Package *extremefit* version 1.0.2 Index]