# Forecasting the number of parties to the TPNW

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*This article shares a statistical forecast of the number of parties to the United Nations Treaty on the Prohibition of Nuclear Weapons. It invites related commentary, encouraging contributors to “be bold but not reckless,” subject to the Wikimedia standards of writing from a neutral point of view, citing credible sources, and raising other questions and concerns on the associated '***“Discuss”'**page.

The accompanying figure displays the history of the number of parties to the United Nations Treaty on the Prohibition of Nuclear Weapons (TPNW) with the median (blue) and 60 and 80 percent confidence limits on number of parties for a certain period in the future in the upper right corner of the plot. The forecasts are based on adding random permutations of the historical interarrival times to the date of the simulation.

The Appendix includes two companion R Markdown vignettes. The older one was used to predict the effective date of the TPNW. On 2020-10-24, Honduras became the fiftieth country to become a party to this treaty. That then fixed the date on which it will enter into force (EIF) as 2021-01-22. A second vignette was then created to document the methodology used to forecast the number of parties at a desired date in the future.

### Statistical theory[edit | edit source]

The time between acceptances, etc., of the TPNW is an example of a renewal process. The simplest renewal process assumes that this renewal time is exponentially distributed, which we assumed for the older vignette.

After the fiftieth ratification, we summarized the bivariate observations on time between dates upon which at least one new party accepted, approved, ratified or acceded to it and then added random permutations of this interarrival distribution to the date of the simulation. This is similar to bootstrapping (statistics). A random permutation will always have the same total simulated time. A bootstrap won't. This made it easier to code random permutations.

## Appendix. Companion R Markdown vignettes[edit | edit source]

Statistical details that make the research in article reproducible are provided in an R Markdown vignette to "Simulate numbers of parties to the TPNW":