Some approximations of the logistic distribution with application to the covariance matrix of logistic regression

In this paper, we show that a two-component normal mixture model provides a good approximation to the logistic distribution. This model is an improvement over using the normal distribution and is comparable with using the t-distribution as approximating distributions. The result from using the mixture model is exemplified by finding an approximative analytic expression for the covariance matrix of logistic regression with normally distributed random regressors.