`BulkAndTails.BulkAndTailsDist`

— TypeBulkAndTailsDist(κ₀,τ₀,ϕ₀,κ₁,τ₁,ϕ₁,ν) The *Bulk-And-Tails (BATs) distribution* has cumulative distribution function

\[F(x) = T_ν(H(x))\]

where T_ν is the student-t cdf with ν degrees of freedom and H is a monotone increasing function. ϕ₀ and ϕ₁ are location parameters for the lower and upper tails. τ₀ and τ₁ are scale parameters for the lower and upper tails. κ₀ and κ₁ are shape parameters for the lower and upper tails. Negative κ indicates a bounded tail. Positive κ indicates a heavy tail. The case κ=0, defined by continuity, indicates a thin Gaussian tail.

`fitbats`

provides maximum likelihood estimation for these parameters. In addition, we provide `pdf`

, `cdf`

, `logpdf`

, `logcdf`

, `quantile`

, and `rand`

functions for `BulkAndTailsDist`

, all of which follow the `Distributions.jl`

framework. We also provide R-friendly versions of these functions and show how to call them from R.

```
BulkAndTailsDist(κ₀,τ₀,ϕ₀,κ₁,τ₁,ϕ₁,ν) # BATs distribution
params(d) # Get the parameters
minimum(d) # lower bound of support
maximum(d) # upper bound of support
```

External links