In probability theory and statistics, the **generalized inverse Gaussian distribution** (**GIG**) is a three-parameter family of continuous probability distributions with probability density function

where *K _{p}* is a modified Bessel function of the second kind,

*a*> 0,

*b*> 0 and

*p*a real parameter. It is used extensively in geostatistics, statistical linguistics, finance, etc. This distribution was first proposed by Étienne Halphen. It was rediscovered and popularised by Ole Barndorff-Nielsen, who called it the generalized inverse Gaussian distribution, and Herbert Sichel. It is also known as the

**Sichel distribution**. Its statistical properties are discussed in Bent Jørgensen's lecture notes.

Read more about Generalized Inverse Gaussian Distribution: Special Cases, Entropy

### Other articles related to "generalized inverse gaussian distribution":

**Generalized Inverse Gaussian Distribution**- Entropy

... The entropy of the

**generalized inverse Gaussian distribution**is given as where is a derivative of the modified Bessel function of the second kind with ...

### Famous quotes containing the words distribution, generalized and/or inverse:

“The man who pretends that the *distribution* of income in this country reflects the *distribution* of ability or character is an ignoramus. The man who says that it could by any possible political device be made to do so is an unpractical visionary. But the man who says that it ought to do so is something worse than an ignoramous and more disastrous than a visionary: he is, in the profoundest Scriptural sense of the word, a fool.”

—George Bernard Shaw (1856–1950)

“One is conscious of no brave and noble earnestness in it, of no *generalized* passion for intellectual and spiritual adventure, of no organized determination to think things out. What is there is a highly self-conscious and insipid correctness, a bloodless respectability submergence of matter in manner—in brief, what is there is the feeble, uninspiring quality of German painting and English music.”

—H.L. (Henry Lewis)

“Yet time and space are but *inverse* measures of the force of the soul. The spirit sports with time.”

—Ralph Waldo Emerson (1803–1882)