I'm trying to generate a Weibull distribution to see if it fits some data. I have an arithmetic mean and variance for this data but I'm struggling to analytically create the specific Weibull parameters from these.
For a Weibull distribution:
σ^2=λ^2 [Γ(1+2/k)-(Γ(1+1/k))^2 ]
I have found that these equations rearrange to:
This can be solved by Wolfram Alpha and with values of μ=7.3151 and σ=4.0730 this gives k=1.8648 and λ=8.2383.
The problem that I'm facing is that I don't understand the jump made by Wolfram from the rearranged equation to the answer. If anyone could offer an explanation that would be great.