Lognormal as special case of generalized gamma

[DEAN FORD]

I cannot follow how the log-normal distribution falls out as a special case of the generalized gamma. I saw the equations on the web site, but I do not understand the step of what happens as lambda goes to zero. Could someone explain the trick to me?

[RS Tech Support]

Actually, the lognormal distribution special case of the generalized gamma is obtained from its original parameterization when k approaches positive infinity. From this formulation and thru further mathematical deduction it can be shown that the generalized gamma yields the lognormal distribution when k approaches infinity (using Stirling’s formula, Taylor series, and L’Hopital’s rule). The following reference provides more information and additional references on the generalized gamma: Meeker and Escobar, Statistical Methods for Reliability Data.