![inverse cdf inverse cdf](https://stephens999.github.io/fiveMinuteStats/figure/inverse_transform_sampling.Rmd/unnamed-chunk-2-1.png)
Using these expectations will give us the value of variance as Similarly the value for n=2 is for alpha greater than 2 Now for the value of α greater than one and n as one In the above integral we used the density function as To get the mean and variance of the inverse gamma distribution using the probability density functionĪnd the definition of expectations, we first find the expectation for any power of x as Mean and variance of the inverse gamma distribution proof
![inverse cdf inverse cdf](https://heds.nz/media/inverse-transform/norm_cdf_2.png)
The mean and variance of the inverse gamma distribution by following the usual definition of expectation and variance will be Mean and variance of the inverse gamma distribution In which the f(x) is the probability density function of the inverse gamma distribution as The cumulative distribution function for the inverse gamma distribution is the distribution function Cumulative distribution function or cdf of inverse gamma distribution The above probability density function in any parameter we can take either in the form of lambda or theta the probability density function which is the reciprocal of gamma distribution is the probability density function of inverse gamma distribution. Thus the random variable with this probability density function is known to be the inverse gamma random variable or inverse gamma distribution or inverted gamma distribution. We take the variable reciprocal or inverse then the probability density function will be If in the gamma distribution in the probability density function inverse gamma distribution | normal inverse gamma distribution The sum of independent gamma distribution is again the gamma distribution with sum of the parameters.The invers gamma distribution can be defined by taking reciprocal of the probability density function of gamma distribution as.