How is a continuous skewed distribution made?

I have a skewed dataset, from which I can calculate median, mean, and standard deviation. I need to fit the data to a continuous probability distribution, however a Gaussian distribution does not capture the skewness of the data.

How could I develop a continuous (skewed) probability distribution given the available information that captures the skewness of the dataset? Is there a formula I could plug into?

• There are many different types of continuous skewed distributions. Can you give more details about your data set? A Cullen-Frey plot is a reasonable place to start. – knrumsey Jul 6 '18 at 22:11
• Sure! I am not sure how to enter in a plot so I will give a few example data points. Dataset is [12.45, 12.5, 12.5, 12.55, 12.55, 12.57, 12.8, 12.97, 13] where as you can see there are a few "outlier" points in 12.8+ that still need to be considered but that skew the distribution over to the right. The median is 12.55 and the mean is 12.65. Ideally the "top" of the distribution would lie over the 12.55 range with a long right tail. – Grassi Jul 6 '18 at 22:23
• If you are willing to provide your data in an accesible manner, or provide a plot, perhaps somebody can help you more. There are lots of good choices however, including Gamma, Weibull and Lognormal. Again, I suggest you look into Cullen-Frey plots for a reasonable starting place (link in comment above). – knrumsey Jul 6 '18 at 22:27
• You may also consider using a tranformed version of your data (maybe log-sinh) to make it normal. Someone should also point out Goodness-Of-Fit in their answer! – Tony Hellmuth Jul 6 '18 at 22:42