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]