Consider a random variable x with a probability density function f(X1; θ) (,where θ is a parameter let X1,X2,…,Xn be a random sample having the same density with joint probability density function
f(X1,X2,…,Xn ; θ)=f(X1; θ).f(X2; θ )….f(Xn; θ)
In this thesis, we will study Akaike information criterion (AIC) introduced by Akaike (1973) as a goodness of fit measure, and study the distribution of AIC of some models using simulation methods.
In chapter one, We will give the definition of AIC and some properties and drawbacks and give the AIC for continuous and discrete models.
Chapter two, gives the exact distribution of AIC in the case of the Normal distribution and in the Exponential distribution. Some times, it is not easy to find the exact distribution of AIC, so we will use simulation methods to find the approximate distribution of AIC in the case of the Normal model, the Cauchy model, and the Student t model, and we will plot the graphs of these distributions.
In chapter three, will study goodness of fit tests, and compare the AIC with the Chi-square methods for goodness of fit. The comparison depends on generated random samples from Normal, Cauchy, and Student T models.
Finally, in chapter four, we take a set of real data that is the distribution of Jordanian population classi- fied by Age and Sex, and test this data as having normal or Gamma distribution using AIC goodness of fit test.