Changes

<math>\mathbf{Q}=\mathbf{{U_{meta}}^T}\mathbf{W}\mathbf{U_{meta}}</math>,

<math>\mathbf{Q}=\mathbf{{U_{meta}}^T}\mathbf{W}\mathbf{U_{meta}}</math>,

where <math>\mathbf{W}</math> is the diagonal matrix of weights of rare variants included in a gene.

where <math>\mathbf{W}</math> is a diagonal matrix of weights of rare variants included in a gene.

As shown in [http://www.ncbi.nlm.nih.gov/pubmed/21737059  '''Wu et. al'''], the null distribution of the <math> \mathbf{Q} </math> statistic follows a mixture chi-sqaured distribution described as

As shown in [http://www.ncbi.nlm.nih.gov/pubmed/21737059  '''Wu et. al'''], the null distribution of the <math> \mathbf{Q} </math> statistic follows a mixture chi-sqaured distribution described as

<math>\mathbf{Q}\sim\sum_{i=1}^m{\lambda_i\chi_{1,i}^2}, </math> where <math>\left(\lambda_1,\lambda_2,\dots,\lambda_m\right)</math> are eigen values of <math>\mathbf{V_{meta}^\frac{1}{2}}\mathbf{W}\mathbf{V_{meta}^\frac{1}{2}}</math>.

<math>\mathbf{Q}\sim\sum_{i=1}^m{\lambda_i\chi_{1,i}^2}, </math> where <math>\left(\lambda_1,\lambda_2,\dots,\lambda_m\right)</math> are eigen values of <math>\mathbf{V_{meta}^\frac{1}{2}}\mathbf{W}\mathbf{V_{meta}^\frac{1}{2}}</math>.