Description Usage Arguments Details Value References See Also Examples

`PPS.fit()`

returns the fit of a PPS distribution to real data, allowing the scale parameter to be held fixed if desired.

1 |

`x` |
a vector of observations |

`estim.method` |
the method of parameter estimation. It may be "MLE", "iMLE", "OLS", or "LMOM". |

`sigma` |
the value of the scale parameter, if it is known; if the value is |

`start` |
a list with the initial values of the parameters for some of the estimation methods. |

`Pareto` |
a logical argument to constrain the PPS fit to a Pareto fit when the value is |

`...` |
other arguments. |

The maximum likelihood method implemented by the direct optimization of the log-likelihood is given by `estim.method = "MLE"`

. The numerical algorithm to search the optimum is the “Nelder-Mead” method implemented in the `optim`

function, considering as initial values those given in the `start`

argument or, if it is missing, those provided by the OLS method.

A different approximation of the maximum likelihood estimates is given by `estim method = "iMLE"`

; it is an iterative methodology where `optimize()`

function provides the optimum scale parameter value, while the `uniroot()`

function solve normal equations for that given scale parameter.

The regression estimates (`"OLS"`

) searchs an optimum scale value (in a OLS criterion) by the `optimize()`

function. Then the rest of the parameters are estimated also by OLS, as appears in Sarabia and Prieto (2009).

In the L-moments method (`"LMOM"`

) estimates are obtained searching parameters that equal the first three sample and theoretical L-moments by means of the “Nelder-Mead” algorithm implemented in `optim()`

; the initial values are given in the `start`

argument or, if it is missing, provided by the `"iMLE"`

.

A `PPSfit`

Object, a list with

estimateparameter estimates.

loglikthe log-likelihood value.

nthe number of observations.

obsthe observations.

obsNamethe name of the variable with the observations.

estim.methodthe method of parameter estimation.

When this last value is `"LMOM"`

the function also returns details about the convergence of the numerical method involved (`convergence`

value).

Sarabia, J.M and Prieto, F. (2009). The Pareto-positive stable distribution: A new descriptive model for city size data, *Physica A: Statistical Mechanics and its Applications*, **388**(19), 4179-4191.
Hosking, J. R. M. (1990). L-moments: analysis and estimation of distributions using linear combinations of order statistics. *Journal of the Royal Statistical Society, Series B*, **52**, 105-124.

`coef.PPSfit`

, `print.PPSfit`

, `plot.PPSfit`

, `GoF`

1 2 3 4 5 6 7 8 9 |

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.