How to Calculate Variance in a Weibull Distribution
- 1). Identify the parameter a in the given Weibull distribution. For example, if you have the equation p(x) = 4(3^-4)(x^(4-1))e^-(x/3)^4, then a = 4. The value of a is the last exponent in the equation.
- 2). Identify the parameter b in the given Weibull distribution. In the equation p(x) = 4(3^-4)(x^(4-1))e^-(x/3)^4, the value of b is 3. The parameter b is the denominator of x in the fraction x/3 that occurs at the end of the expression.
- 3). Determine G(1 + 2/a) using your value of a and software that can compute Gamma functions. Using a = 4, you must calculate G(1.5). Using a calculator or software, you obtain G(1.5) = 0.886227.
- 4). Compute G(1 + 1/a)^2 using the same value of a. For instance, since a = 4, you must find G(1.25)^2, which equals 0.821565
- 5). Subtract the value you obtained in Step 4 from the value you obtained in Step 3. For example, you calculate 0.886227 - 0.821565 = 0.064662.
- 6). Multiply this number by b^2. This is the variance of the Weibull distribution. For instance, since b = 3, you compute (3^2)*(0.064662) = 0.581958 as the variance.
