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The plot below models a sample of departure delays of flights, the x-axis is minutes delayed. The mean is about 10 (red line) and std is 36. The distribution has a very long tail (some flights are 800 minute delayed). The blue line is a fitted normal (mean=10, std=36) and the purple distribution is a shifted Poison (such that it can handle negative values).

Both of them completely miss the data as the data has a long tail and is very skewed. How might I model the probability of flight delays best?

skewed dataset

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  • $\begingroup$ I've also tried fitting a skewed normal, but it is also not fully capturing the dataset. $\endgroup$ Mar 12 at 23:00
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    $\begingroup$ Your question will be better answered if you describe the reason for needing a parametric function. (Not suggesting you don't have a reason. It's just not given.) Why not just fit a nonparametric density function? $\endgroup$
    – JimB
    Mar 13 at 5:15
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    $\begingroup$ You could perhaps consider a location-scale version of a non-central Student $t$-distribution which has 4 parameters (one more than the skew normal). Yet another alternative is the variance-gamma distribution, en.wikipedia.org/wiki/Variance-gamma_distribution $\endgroup$ Mar 13 at 9:41

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