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Inverse Gamma Distribution is a reciprocal of gamma probability density function with positive shape parameters $ {alpha, beta } $ and location parameter $ { mu } $. $ {alpha } $ controls the height. Higher the $ {alpha } $, taller is the probability density function (PDF). $ {beta } $ controls the speed. It is defined by following formula.
Formula
${ f(x) = frac{x^{-(alpha+1)}e^{frac{-1}{beta x}}}{ Gamma(alpha) beta^alpha} \[7pt]
, where x gt 0 }$
Where −
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${alpha}$ = positive shape parameter.
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${beta}$ = positive shape parameter.
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${x}$ = random variable.
Following diagram shows the probability density function with different parameter combinations.
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