Continuous Random Variables we are working with commonly use

Continuous Random Variables

we are working with commonly used discrete and continuous distribution

We want to use a gamma distribution to model and forecast the monthly rainfall in inches. In order to identify the gamma distribution, we can estimate the value of parameters a and beta from the mean and variance based on past data. It is known to us that the mean rainfall is 4.12 and variance is 6.33. Calculate the estimated alpha and beta ?.

Solution

We have mean = /

                 Variance = /²

Given mean = 4.12

       Variance = 6.33

Mean = / =4.12

        = /4.12

variance = /² = 6.33

   /( /4.12)² =6.33

*(4.12)/ ² = 6.33

= 2.6816

  = /4.12

  = 2.6816/4.12

  = 0.6509