Reason generalized linear model

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Often one says that the Generalized linear models are 'invented' such that it is possible that the variance depends on the mean. Unfortunatly , I can't find a real-life example where this is wanted. Can someone help me with this?

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Take for instance the Poisson regression, when if there is no over-dispersion, you expect the mean to be equal the variance. So, if this kind model really fits your data, the realm of possible application is enormous. For instance, the Challenger data.