Give Units to Any Distribution

Create a distribution of arrival time in seconds from distribution of its magnitude.

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\[ScriptCapitalD] = QuantityDistribution[ExponentialDistribution[3], "Seconds"]

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Use QuantityUnit and QuantityMagnitude to extract the unit of the associated random variate and the distribution of its magnitude.

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QuantityUnit[\[ScriptCapitalD]]

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QuantityMagnitude[\[ScriptCapitalD]]

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Any distribution, including formula distributions, derived distributions, etc., can be used as the distribution of the magnitude.

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mag\[ScriptCapitalD] = ProbabilityDistribution[{"HF", x}, {x, 0, \[Infinity]}];

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lifetime\[ScriptCapitalD] = QuantityDistribution[mag\[ScriptCapitalD], "Hours"]

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