Distributions differ from {invgamma} / {truncdist}

[fkohrt]

I tried to update a density plot created with {invgamma} and {truncdist} to use {distributional}, but the resulting distributions seem to differ. See the following comparison between the original (black) and the reproduced (red) density plot.

library(invgamma)

x <- seq(5, 400, by=1)
y_truncdist <- truncdist::dtrunc(x,
                                 spec = "invgamma",
                                 shape = 1.15326986,
                                 scale = 0.04622745,
                                 a = 5,
                                 b = 1905)
y_distributional <- distributional::dist_inverse_gamma(shape = 1.15326986,
                                                       scale = 0.04622745) |>
  distributional::dist_truncated(lower = 5, upper = 1905) |>
  density(at = x) |>
  getElement(1)
plot(x, y_distributional, type="n") 
lines(x, y_truncdist, type="l", col="black", lwd=3)
lines(x, y_distributional, type="l", col="red", lwd=3)

sessionInfo()

``` R version 4.1.3 (2022-03-10) Platform: x86_64-redhat-linux-gnu (64-bit) Running under: Fedora Linux 36 (Workstation Edition) Matrix products: default BLAS/LAPACK: /usr/lib64/libflexiblas.so.3.2 locale: [1] LC_CTYPE=en_US.UTF-8 [2] LC_NUMERIC=C [3] LC_TIME=de_DE.UTF-8 [4] LC_COLLATE=en_US.UTF-8 [5] LC_MONETARY=de_DE.UTF-8 [6] LC_MESSAGES=en_US.UTF-8 [7] LC_PAPER=de_DE.UTF-8 [8] LC_NAME=C [9] LC_ADDRESS=C [10] LC_TELEPHONE=C [11] LC_MEASUREMENT=de_DE.UTF-8 [12] LC_IDENTIFICATION=C attached base packages: [1] stats graphics grDevices datasets [5] utils methods base other attached packages: [1] invgamma_1.1 loaded via a namespace (and not attached): [1] rstudioapi_0.14 magrittr_2.0.3 [3] expint_0.1-7 tidyselect_1.2.0 [5] evd_2.3-3 munsell_0.5.0 [7] colorspace_2.0-3 colorDF_0.1.7 [9] R6_2.5.1 rlang_1.0.6 [11] fansi_1.0.3 actuar_3.3-0 [13] dplyr_1.0.10 CoprManager_0.3.10 [15] tools_4.1.3 truncdist_1.0-2 [17] grid_4.1.3 gtable_0.3.1 [19] utf8_1.2.2 DBI_1.1.3 [21] cli_3.4.1 assertthat_0.2.1 [23] tibble_3.1.8 lifecycle_1.0.3 [25] crayon_1.5.2 purrr_0.3.5 [27] farver_2.1.1 ggplot2_3.3.6 [29] vctrs_0.4.2 glue_1.6.2 [31] compiler_4.1.3 pillar_1.8.1 [33] generics_0.1.3 scales_1.2.1 [35] stats4_4.1.3 distributional_0.3.1 [37] pkgconfig_2.0.3 ```

[fkohrt]

@mitchelloharawild I have identified the reason for the difference: {invgamma} has different semantics for its parameters and leads to the same results as {distributional} when setting scale = 1 / ….

See also dkahle/invgamma#1

[dkahle]

Thought I'd tag this response here for future readers. TL;DR: the parameters in invgamma refer to the parameters of the pre-transformed distribution functions, e.g. dgamma().

Fuller explanation here. Sorry for the confusion!