Why does the inverse pareto distribution have a high likelihood for the Boron data compared to the default distributions?

``` r
library(ssdtools)

data <- ssddata::ccme_boron
k <- 2
n <- nrow(data)

fit <- ssd_fit_dists(data, dists = c("invpareto", "weibull"))
autoplot(fit)
```


``` r

glance(fit)
#> # A tibble: 2 × 8
#> dist npars nobs log_lik aic aicc delta weight
#>
#> 1 invpareto 2 28 -116. 235. 236. 0 0.781
#> 2 weibull 2 28 -117. 238. 238. 2.54 0.219
logLik(fit)
#> invpareto weibull
#> -115.5439 -116.8126

AIC <- 2 * (k - logLik(fit))
AIC
#> invpareto weibull
#> 235.0879 237.6253

AICc <- AIC + (2 * k^2 + 2 * k) / (n - k - 1)
AICc
#> invpareto weibull
#> 235.5679 238.1053

coef <- coef(fit)
scale <- coef$est[coef$dist == "invpareto" & coef$term == "scale"]
shape <- coef$est[coef$dist == "invpareto" & coef$term == "shape"]

# as currently calculated by ssdtools
sum(log(shape) - shape*log(scale) + (shape+1)*log(data$Conc) - 2*log(data$Conc))
#> [1] -115.5439
```

^{Created on 2024-12-12 with [reprex v2.1.1](https://reprex.tidyverse.org)}

Reproduce the Boron example with ssd_fit_dists(data, dists = c("invpareto", "weibull")) and inspect the resulting glance(), logLik(), and coef() values. Trace how the invpareto likelihood and AIC/AICc are calculated, then compare those calculations with weibull. Done means explaining whether the higher invpareto likelihood is correct or identifying the calculation that needs correction.

Written by the indexing model from the issue text.