When the probability of observing a large positive error is larger than the probability of observing a large negative error in binary classification, how can this be modelled by a skewed noise distribution using the maximum likelihood approach?

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From page 103 of: http://smlbook.org/book/sml-book-draft-latest.pdf

"Using the maximum likelihood approach, other assumptions about the noise or insights into its distribution can be incorporated in a similar way in the regression model (5.1). For instance, if we believe that the error is non-symmetric, in the sense that the probability of observing a large positive error is larger than the probability of observing a large negative error, then this can be modelled by a skewed noise distribution. Using the negative log-likelihood loss is then a systematic way of incorporating this skewness into the training objective."