clauset.xmax {distributionsrd} | R Documentation |

## Pareto scale determination à la Clauset

### Description

This method determines the optimal scale parameter of the Inverse Pareto distribution using the iterative method (Clauset et al. 2009) that minimizes the Kolmogorov-Smirnov distance.

### Usage

```
clauset.xmax(x, q = 1)
```

### Arguments

`x` |
data vector |

`q` |
Percentage of data to search over (starting from the smallest values) |

### Value

Returns a named list containing a

- coefficients
Named vector of coefficients

- KS
Minimum Kolmogorov-Smirnov distance

- n
Number of observations in the Inverse Pareto tail

- coeff.evo
Evolution of the Inverse Pareto shape parameter over the iterations

### References

Clauset A, Shalizi CR, Newman ME (2009).
“Power-law distributions in empirical data.”
*SIAM review*, **51**(4), 661–703.

### Examples

```
## Determine cuttof from compostie InvPareto-Lognormal distribution using Clauset's method
dist <- c("invpareto", "lnorm")
coeff <- c(coeff1.k = 1.5, coeff2.meanlog = 1, coeff2.sdlog = 0.5)
x <- rcomposite(1e3, dist = dist, coeff = coeff)
out <- clauset.xmax(x = x)
out$coefficients
coeffcomposite(dist = dist, coeff = coeff, startc = c(1, 1))$coeff1
## Speed up method by considering values above certain quantile only
dist <- c("invpareto", "lnorm")
coeff <- c(coeff1.k = 1.5, coeff2.meanlog = 1, coeff2.sdlog = 0.5)
x <- rcomposite(1e3, dist = dist, coeff = coeff)
out <- clauset.xmax(x = x, q = 0.5)
out$coefficients
coeffcomposite(dist = dist, coeff = coeff, startc = c(1, 1))$coeff1
```

[Package

*distributionsrd*version 0.0.6 Index]