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- Want to know if range of hotel stay in days satisfies given bound

Ok, so I'm given hotel data :{Arrival Date, Departure Date}, each in terms of nth day of the year , and I want to estimate whether the range/difference, aka, the length of stay is below a bound. Say a week ( 7 days) for definiteness.

I'm thinking of using either the distribution of the range or to use order statistics for the auxiliary variable Difference in Dates := D= Departure Date - Arrival Date and use the distribution of the range ##D_{Max}- D_{Min}##, or maybe just the distribution of the Max.

Is this a good way?

Thing is I don't know the distribution of neither Arrival Date nor of Departure Date, so I don't see how to compute the distribution of any of these 3: Max Departure, Min Arrival, Max Departure- Min Arrival, to compute the order statistics.

Maybe @StephenTashi can comment?

I'm thinking of using either the distribution of the range or to use order statistics for the auxiliary variable Difference in Dates := D= Departure Date - Arrival Date and use the distribution of the range ##D_{Max}- D_{Min}##, or maybe just the distribution of the Max.

Is this a good way?

Thing is I don't know the distribution of neither Arrival Date nor of Departure Date, so I don't see how to compute the distribution of any of these 3: Max Departure, Min Arrival, Max Departure- Min Arrival, to compute the order statistics.

Maybe @StephenTashi can comment?

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