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Is there any global database that enables the stochastic analysis of questions such as age distribution of fatalities, etc?

A Google search produced only a WHO article database: https://www.who.int/emergencies/diseases/novel-coronavirus-2019/global-research-on-novel-coronavirus-2019-ncov

Update:

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I recommend this github project from the Johns Hopkins University Center for Systems Science and Engineering (JHU CSSE):

https://github.com/CSSEGISandData/COVID-19

They collect the official numbers from different organizations and ministries from all over the world and update their repository every day.
They don't provide information about the age of patients though.

There is a Japanese project, however, which provides also some age information:
https://covid19japan.com/
But the Japanese people seem to be very disciplined and have a very low infection rate at the moment.

Update:
I found a database with German Covid-19 cases including age information:
https://npgeo-corona-npgeo-de.hub.arcgis.com/datasets/dd4580c810204019a7b8eb3e0b329dd6_0

From the same company (ESRI) there are a lot more data sets online also for Covid-19. One might have to search for age information, though.
https://coronavirus-resources.esri.com/

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You can find a collection of data that is updated on a daily basis on github. There is also included some code

https://github.com/globalcitizen/2019-wuhan-coronavirus-data

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Kaggle has an ongoing competition analysing COVID-19 related medical literature. This competition provides a large dataset, as well as already published analysis tools and other assistance to get you started.

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Additionaly to Philipp Leitl's answer: Overview of cases in Italy, provided by Instituto Superiore Di Sanita, updated on a daily basis (just change the date in the url) with death distribution by age: https://www.epicentro.iss.it/coronavirus/bollettino/Infografica_27marzo%20ENG.pdf The korean Korea Centers for Disease Control and Prevention also publish some data on a daly basis, including case distribution by gender and age: https://www.cdc.go.kr/board/board.es?mid=a30402000000&bid=0030 For example, press release No 215, 26.3.2020: https://www.cdc.go.kr/board/board.es?mid=a30402000000&bid=0030&act=view&list_no=366650&tag=&nPage=1

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http://go.usa.gov/xdbuc Select a dataset and click Download button. You can choose Fasta format

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