# Modelling a right-long-tailed distribution

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?

• I've also tried fitting a skewed normal, but it is also not fully capturing the dataset. Mar 12 at 23:00
• 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?
– JimB
Mar 13 at 5:15
• 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 Mar 13 at 9:41