Last updated: 2025-09-02
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Knit directory: muse/
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| File | Version | Author | Date | Message |
|---|---|---|---|---|
| Rmd | 3160792 | Dave Tang | 2025-09-02 | Gamma distribution |
| html | 779b385 | Dave Tang | 2025-09-02 | Build site. |
| Rmd | 5a74914 | Dave Tang | 2025-09-02 | Fitting a distribution |
When a “distribution was fit to” something, it means that we assume that the data comes from some probability distribution and we are estimating the distribution’s parameters from the data so that the model best represents the observed values.
Suppose we have some data:
set.seed(1984)
eg1 <- rnorm(100, mean = 5, sd = 2)Fit a Normal distribution.
eg1_fit <- MASS::fitdistr(eg1, "normal")
eg1_fit mean sd
5.062545 1.873380
(0.187338) (0.132468)A Normal distribution was fit to eg1, with estimated
mean 5.0625454 and standard deviation 1.8733798
Poisson.
set.seed(1984)
eg2 <- rpois(100, lambda = 3)
eg2_fit <- MASS::fitdistr(eg2, "Poisson")
eg2_fit lambda
3.1000000
(0.1760682)set.seed(1984)
eg3 <- stats::rgamma(300, shape = 2, rate = 3, scale = 1/3)Warning in stats::rgamma(300, shape = 2, rate = 3, scale = 1/3): specify 'rate'
or 'scale' but not botheg3_fit <- MASS::fitdistr(eg3, "gamma")Warning in densfun(x, parm[1], parm[2], ...): NaNs producedeg3_fit shape rate
2.0425966 3.1910159
(0.1550892) (0.2744437)Akaike Information Criterion (AIC) is an estimator of prediction error and thereby relative quality of statistical models for a given set of data. Put simply, it’s a measure of how well a statistical model fits the data, but with a built-in penalty for model complexity. When comparing models, the one with the lowest AIC is preferred.
set.seed(1984)
eg1 <- rnorm(100, mean = 5, sd = 2)
eg1_norm <- MASS::fitdistr(eg1, "normal")
eg1_exp <- MASS::fitdistr(eg1, "exponential")
stats::AIC(eg1_norm, eg1_exp) df AIC
eg1_norm 2 413.3365
eg1_exp 1 526.3739
sessionInfo()R version 4.5.0 (2025-04-11)
Platform: x86_64-pc-linux-gnu
Running under: Ubuntu 24.04.2 LTS
Matrix products: default
BLAS: /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3
LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so; LAPACK version 3.12.0
locale:
[1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
[3] LC_TIME=en_US.UTF-8 LC_COLLATE=en_US.UTF-8
[5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
[7] LC_PAPER=en_US.UTF-8 LC_NAME=C
[9] LC_ADDRESS=C LC_TELEPHONE=C
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
time zone: Etc/UTC
tzcode source: system (glibc)
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] MASS_7.3-65 workflowr_1.7.1
loaded via a namespace (and not attached):
[1] vctrs_0.6.5 httr_1.4.7 cli_3.6.5 knitr_1.50
[5] rlang_1.1.6 xfun_0.52 stringi_1.8.7 processx_3.8.6
[9] promises_1.3.2 jsonlite_2.0.0 glue_1.8.0 rprojroot_2.0.4
[13] git2r_0.36.2 htmltools_0.5.8.1 httpuv_1.6.16 ps_1.9.1
[17] sass_0.4.10 rmarkdown_2.29 jquerylib_0.1.4 tibble_3.2.1
[21] evaluate_1.0.3 fastmap_1.2.0 yaml_2.3.10 lifecycle_1.0.4
[25] whisker_0.4.1 stringr_1.5.1 compiler_4.5.0 fs_1.6.6
[29] pkgconfig_2.0.3 Rcpp_1.0.14 rstudioapi_0.17.1 later_1.4.2
[33] digest_0.6.37 R6_2.6.1 pillar_1.10.2 callr_3.7.6
[37] magrittr_2.0.3 bslib_0.9.0 tools_4.5.0 cachem_1.1.0
[41] getPass_0.2-4