STAT4290 April 27 2011

STAT4290 April 27 2011 - Chi-square text for goodness of...

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Chi-square text for goodness of fit Separate into c classes Question: how effective should this be for: (i) Continuous distribution? (Not so clear – run the risk of loss of power/loss of information, when we take the continuous values and discretize or categorize them. How do we do the split? How many classes? How b*j are they? Etc. (ii) Discrete distribution? (Probably should be ok b/c classes reflect something intrinsic to the distribution. A small number of large (span a wider range of values) classes -> loss of information. A large number of small classes -> lose less information, but test may not be valid if too many of the Ej are small (< 5) An advantage of the chi-square procedure (compared to Kolmogorov): if the distribution is not completely specified under Ho, but only up to a number k of parameters, the chi- square goodness of fit test is easy enough to modify. The usual procedure is to estimate each of the parameter (e.g. Poisson rate “lambda”, or normal mean and variance “mu” and “sigma^2”, etc) use those to calculate the Ej, and
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STAT4290 April 27 2011 - Chi-square text for goodness of...

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