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Are there any methods to test if some real world data follows the memoryless property? For example, are there any statistical hypothesis tests that can be used to check if the data is truly "memoryless"? I have often seen mathematical statements that describe the memoryless condition - but I have never seen any methods to actually check if real world data is actually memoryless.

Is this possible?

Thanks

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The only continuous distribution that is memoryless is the exponential distribution. Similarly, the only discrete distribution that is memoryless is the geometric distribution.

If you plot your data and fit an exponential/geometric distribution, you could visually assess whether those distributions could plausibly represent the data. If so, there is a good argument for considering the data to be memoryless.

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