Te model will have three inputs sigma1 sigma2nbsp and q

Question

Create a Mixture of Gaussians in Excel Method One: Random Variable Approach

The model will have three inputs σ₁, σ₂ , and q (assume means of zero): Use the inverse transform method to create two series of normal variables with standard deviations of σ₁ and σ₂ , each involving a series of calls to RAND(). Then, use a third series of calls to RAND () to determine which of the two normal variables just created make up the mixture,

• Generate at least 65,000 numbers.
• Calculate the mean, standard deviation, and excess kurtosis for all three distributions.
• Check the resultant mixture versus the theoretical formulas for convergence.

This approach directly models the mixed Gaussian density function rather than the random numbers themselves.

• The model will have three inputs (assume means of zero): σ₁, σ₂, and q.
• Choose the discretized x-space carefully.
• Graph all three distributions.
• Use the density approach formulas for the moments (3.64)-(3.66) and check them against the theoretical values. If the match is poor, it could be due to a poor choice of the discretized x-space.