From the introduction: Consider the mixture of two Pareto distributions given by the pdf \[ f(x)=\alpha\theta a^\theta/ x^{\theta+1}+(1-\alpha)\varphi a^\varphi/x^{\varphi+1}\tag{1} \] for \(x\geq a\), \(a>0\), \(\theta>0\), \(\varphi>0\), \(0<\alpha<1\), and assume without loss of generality that \(\theta>\varphi\). This distribution is also known as the double Pareto distribution. It has been used for statistical analysis of the airport network of China, and as models for distributions for human settlements, income, and size distributions.
The aim of this note is to calculate the Fisher information matrix corresponding to (1) and to provide useful numerical tabulations of the matrix (we also provide the estimation procedures by the method of maximum likelihood).